Spectroscopic Detection of Primordial Black Hole Hydrogen-like Atoms?

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Background Building on theoretical work proposing that gravitational binding between primordial black holes and electrons may create exotic quantum systems, we investigate the observational prospects for these hypothetical atomic structures. Methods We develop a comprehensive detection framework combining simulated spectroscopic signatures, sensitivity analyses for current space-based infrared telescopes, and machine-learning classification algorithms to distinguish genuine signals from astrophysical contaminants. Our approach integrates deep spectroscopic surveys targeting dark matter halos, multi-messenger coordination with gravitational wave triggers, and time-domain analysis of spectral evolution. Results Our simulations predict that PBH-H protoatoms would emit characteristic far-infrared transitions spanning one to fifty micrometers, with the dominant n equals two to n equals one line occurring at five point four micrometers, placing it within the detection range of the James Webb Space Telescope Mid-Infrared Instrument. The spectral features exhibit significant broadening from Hawking radiation-induced quantum blur and rapid temporal evolution on timescales of minutes to hours as electrons spiral toward the black hole nuclei. Sensitivity analysis confirms that the James Webb Space Telescope can probe PBH-H densities as low as one thousand per cubic parsec in the Galactic Center, while the Atacama Large Millimeter Array and Very Large Array can access higher-order millimeter and centimeter wavelength transitions. Conclusions Successful detection of PBH-H protoatoms would validate primordial black holes as dark matter constituents and provide unprecedented tests of quantum gravity at atomic scales, representing a transformative advancement in understanding dark matter composition and quantum gravitational phenomena. " } { "@context": "http://schema.org", "@type": "BreadcrumbList", "itemListElement": [ { "@type": "ListItem", "position": "1", "item": { "@id": "https://f1000research.com/", "name": "Home" } }, { "@type": "ListItem", "position": "2", "item": { "@id": "https://f1000research.com/browse/articles", "name": "Browse" } }, { "@type": "ListItem", "position": "3", "item": { "@id": "https://f1000research.com/articles/15-322/v1", "name": "Spectroscopic Detection of Primordial Black Hole Hydrogen-like Atoms?" } } ] } Home Browse Spectroscopic Detection of Primordial Black Hole Hydrogen-like Atoms? ALL Metrics - Views Downloads Get PDF Get XML Cite How to cite this article Quiroga E. Spectroscopic Detection of Primordial Black Hole Hydrogen-like Atoms? [version 1; peer review: 2 not approved] . F1000Research 2026, 15 :322 ( https://doi.org/10.12688/f1000research.177351.1 ) NOTE: If applicable, it is important to ensure the information in square brackets after the title is included in all citations of this article. Close Copy Citation Details Export Export Citation Sciwheel EndNote Ref. Manager Bibtex ProCite Sente EXPORT Select a format first Track Share ▬ ✚ Research Article Spectroscopic Detection of Primordial Black Hole Hydrogen-like Atoms? [version 1; peer review: 2 not approved] Elio Quiroga https://orcid.org/0000-0002-4912-1941 Elio Quiroga https://orcid.org/0000-0002-4912-1941 PUBLISHED 25 Feb 2026 Author details Author details Universidad del Atlantico Medio, Las Palmas de Gran Canaria, Canary Islands, Spain Elio Quiroga Roles: Conceptualization, Investigation, Methodology, Software, Writing – Original Draft Preparation, Writing – Review & Editing OPEN PEER REVIEW DETAILS REVIEWER STATUS Abstract This paper explores whether primordial black hole hydrogen-like atoms (PBH-H protoatoms) could be detectable through their distinctive spectroscopic signatures. Background Building on theoretical work proposing that gravitational binding between primordial black holes and electrons may create exotic quantum systems, we investigate the observational prospects for these hypothetical atomic structures. Methods We develop a comprehensive detection framework combining simulated spectroscopic signatures, sensitivity analyses for current space-based infrared telescopes, and machine-learning classification algorithms to distinguish genuine signals from astrophysical contaminants. Our approach integrates deep spectroscopic surveys targeting dark matter halos, multi-messenger coordination with gravitational wave triggers, and time-domain analysis of spectral evolution. Results Our simulations predict that PBH-H protoatoms would emit characteristic far-infrared transitions spanning one to fifty micrometers, with the dominant n equals two to n equals one line occurring at five point four micrometers, placing it within the detection range of the James Webb Space Telescope Mid-Infrared Instrument. The spectral features exhibit significant broadening from Hawking radiation-induced quantum blur and rapid temporal evolution on timescales of minutes to hours as electrons spiral toward the black hole nuclei. Sensitivity analysis confirms that the James Webb Space Telescope can probe PBH-H densities as low as one thousand per cubic parsec in the Galactic Center, while the Atacama Large Millimeter Array and Very Large Array can access higher-order millimeter and centimeter wavelength transitions. Conclusions Successful detection of PBH-H protoatoms would validate primordial black holes as dark matter constituents and provide unprecedented tests of quantum gravity at atomic scales, representing a transformative advancement in understanding dark matter composition and quantum gravitational phenomena. READ ALL READ LESS Keywords Primordial black holes; Dark matter spectroscopy; Quantum gravity phenomenology; James Webb Space Telescope; Hawking radiation; Multi-messenger astronomy Corresponding Author(s) Elio Quiroga ( [email protected] ) Close Corresponding author: Elio Quiroga Competing interests: No competing interests were disclosed. Grant information: The author(s) declared that no grants were involved in supporting this work. Copyright: © 2026 Quiroga E. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. How to cite: Quiroga E. Spectroscopic Detection of Primordial Black Hole Hydrogen-like Atoms? [version 1; peer review: 2 not approved] . F1000Research 2026, 15 :322 ( https://doi.org/10.12688/f1000research.177351.1 ) First published: 25 Feb 2026, 15 :322 ( https://doi.org/10.12688/f1000research.177351.1 ) Latest published: 16 Apr 2026, 15 :322 ( https://doi.org/10.12688/f1000research.177351.2 )  There is a newer version of this article available. Suppress this message for one day. Introduction The theoretical framework for this paper was presented by the author in a previous study of primordial black hole hydrogen-like atoms (PBH-H protoatoms; in Quiroga Rodríguez, 2024 ). This theoretical paper explores the concept of “quantum gravitational atoms” or “PBH--H protoatoms,” where a primordial black hole, or PBH ( Carr & Hawking, 1974 ) with a mass of 5.7×10 14 g (≈5.7×10 11 kg) 1 replaces the nucleus in a hydrogen-like atom. The study investigates whether such a PBH could capture a proton within its event horizon, forming a positively charged nucleus, and subsequently bind an electron in orbit via gravitational attraction, analogous to the electromagnetic binding in hydrogen. Key calculations reveal a ground-state binding energy of −0.31 eV, approximately 44 times weaker than standard hydrogen (−13.6 eV), due to the substitution of gravity for electromagnetism in the potential. This extremely low binding energy implies the electron is highly susceptible to excitation, ionization, or environmental perturbations, rendering the protoatom “ultra-reactive” with potentially novel chemical properties. However, stability is challenged by Hawking radiation from the PBH ( Hawking, 1975 ), which emits at temperatures (∼18.5 MeV) far exceeding the binding energy and enabling electron-positron pair creation, likely disrupting the bound state. The Bohr radius (0.5290.529 Å) remains similar to hydrogen, and the PBH’s Schwarzschild radius (8.45×10 −16 m) is smaller than this orbital distance, preventing immediate electron accretion—though quantum effects or radiation losses could lead to eventual absorption. The paper suggested falsifiable predictions: detecting unique electromagnetic signatures from electron transitions or accretion could confirm PBH protoatoms or constrain their abundance and role in dark matter ( Carr et al., 2021 ). On the other hand, the author recognizes a critical oversight in the initial treatment of a charged PBH. For a PBH possessing a net charge of +1, the dominant binding force with an electron is electrostatic, not gravitational. The gravitational contribution is negligible in comparison, representing only approximately 15% of the total potential. Consequently, the system’s ground state energy and Bohr radius are indeed effectively identical to those of standard hydrogen, as the electrostatic potential dictates the binding. The exotic nature and detectability of such a “PBH-hydrogen atom” therefore do not stem from an altered ground state, but rather from the unique nuclear environment—specifically, the intense Hawking radiation field and the eventual quantum gravitational effects near the event horizon—which would profoundly influence the atom’s stability, spectral line profiles, and temporal evolution. This work continues que task and proposes a speculative approach to detecting PBH-H atoms through spectroscopic signatures. The implications of successfully detecting these exotic atomic structures would help to change our understanding of quantum gravity, dark matter composition ( Bird et al., 2023 ), and the early universe’s physical conditions. Methods The theoretical foundation for PBH-H protoatoms rests on the possibility that primordial black holes could capture and bind electrons through gravitational forces, creating hydrogen-like atomic structures where gravity replaces electromagnetic interactions as the primary binding mechanism. These hypothetical objects would possess a binding energy of approximately -0.31 eV, representing a binding strength that is 44 times weaker than conventional hydrogen atoms. This dramatic reduction in binding energy fundamentally alters the spectroscopic properties of these systems, shifting their characteristic emission and absorption lines from the ultraviolet and visible regions of the electromagnetic spectrum to the far-infrared and microwave domains. An that may be an excellent clue to find them. The spectroscopic simulation reveals that PBH-H protoatoms would exhibit their primary spectral features in the wavelength range extending from approximately 1 to 50 micrometers, with the most prominent transitions occurring at specific wavelengths that correspond to electron transitions between quantum energy levels. The n = 2 to n = 1 transition, representing the strongest spectroscopic signature, would manifest at approximately 5.4 micrometers, placing it probably near the observational capabilities of advanced infrared space telescopes. Higher-order transitions, including the n = 3 to n = 1 transition at 12.1 micrometers, the n = 4 to n = 1 transition at 21.5 micrometers, and the n = 5 to n = 1 transition at 33.6 micrometers, would create a distinctive spectroscopic fingerprint that could serve as definitive evidence for the existence of these exotic atomic systems. The energy level diagram shown in Figure 1 (left: PBH-H, right: normal hydrogen) shows that the PBH-H protoatom exhibits much shallower binding energies compared to hydrogen, with a ground state energy of approximately −0.31 eV for PBH-H versus −13.6 eV for hydrogen. Additionally, the energy level spacing in PBH-H is tighter, shifting transitions toward the far-infrared. Figure 1. Energy level comparison between a PBH-H and normal hydrogen. The energy level structure of PBH-H protoatoms differs fundamentally from conventional atomic systems due to the replacement of Coulomb interactions with gravitational binding forces, as explained in the first paper. While the Bohr radius remains approximately unchanged at 0.529 angstroms due to the specific mass relationships involved, the energy spacing between quantum levels becomes dramatically compressed. This compression results in spectral lines that are not only shifted to longer wavelengths but also significantly broadened due to the enhanced sensitivity of these weakly bound systems to environmental perturbations. The gravitational binding creates atomic systems that are extraordinarily reactive to external influences, making them highly susceptible to ionization and excitation by cosmic radiation, thermal fluctuations, and electromagnetic fields that would have negligible effects on normal atoms. The PBH-H spectrum shown in Figure 2 has broad features in the 1–50 μm range, with line blending and a background from Hawking radiation ( Coogan et al., 2021 ), whereas the normal hydrogen spectrum is concentrated in the ultraviolet to visible (~0.1–1 μm) range. A combined log-scale plot reveals the contrast in intensity and spectral distribution between the two. Figure 2. Simulated spectroscopy signatures for PBH-H protoatoms. The apparent discrepancy in the visualized line width between figures is primarily a consequence of the different plotting contexts and purposes. The spectrum in Figure 2 is a simulated representation of the cumulative emission from a population of PBH-H atoms, intentionally illustrating the significant broadening mechanisms at play. This broadening is simulated using a Voigt profile approximation, convolving contributions from several physical processes: intrinsic thermal Doppler broadening due to the kinetic temperature of the bound electrons, pressure broadening from the intense local radiation field, and most critically, the fundamental “quantum blur” induced by the interaction with the high-energy Hawking radiation field, which disrupts well-defined energy levels. The plot in Figure 3 compares the synthetic spectra of PBH-H protoatoms for various primordial black hole (PBH) masses, ranging from 1 × 10 11 kg to 3 × 10 12 kg. As the PBH mass increases ( Dasgupta et al., 2021 ), the binding energy becomes stronger, shifting spectral features toward shorter wavelengths (leftward in the plot). Lower-mass PBHs produce broader, lower-energy spectral lines in the far-infrared to mid-infrared region, while the original case (5.7 × 10 11 kg) commented in the original paper, lies in the middle, with transitions spanning approximately 5–40 μm. A crucial question is the evaporation. Primordial black holes (PBHs) with masses below approximately 10 11 –10 12 kg would have already evaporated before the present, as their Hawking lifetimes are too short. However, lifetimes increase sharply with mass: a PBH of 10 12 kg has a lifespan of around 10 9 years, while those with masses of 10 13 kg or more can survive longer than the current age of the universe. Figure 3. PBH-H spectra for different PBH masses. Figure 4 plots the visual summary of PBH number estimates: the X-axis (log scale) represents PBH mass from 10 10 kg to 10 15 kg, while the Y-axis (log scale) shows the estimated number of PBHs. Two curves are presented: a yellow solid line for PBHs within the Milky Way halo and an orange dashed line for those within the entire observable universe. It presents our original visual summary of PBH population estimates, constructed from a synthesis of current observational constraints on their abundance as a function of mass. The curves are not direct data but a schematic representation based on the upper limits derived from microlensing surveys (e.g., OGLE, HSC), CMB anisotropy measurements, and galactic gamma-ray backgrounds, which collectively severely constrain PBH populations across many mass windows. The plotted estimates for the Milky Way halo and the observable universe are extrapolations assuming a monochromatic mass function and that PBHs constitute a fraction of the dark matter density at the level currently permitted by these constraints. This visualization is intended to contextualize the potential scale of the population for the mass range of interest and underscore that, even under tight limits, a non-zero abundance remains possible, leading to a potentially vast number of low-mass objects. A more detailed statistical analysis incorporating extended mass functions and full constraint datasets is beyond the scope of this initial proposal but is an essential next step for refining detection prospects. Figure 4. PBH population estimates under observational constraints. While standard Hawking evaporation models indicate that PBHs below ~10 13 kg should have fully evaporated by now—posing a clear constraint on their survival—this work proceeds under the assumption that a population of lower-mass PBHs may still persist. Some studies have proposed that evaporation may not proceed as rapidly as originally thought, particularly under scenarios involving quantum gravitational effects or interactions with surrounding matter fields, which could prolong their lifetimes beyond the canonical predictions ( Haque et al., 2024 ; Dvali et al., 2025 ). This still speculative assumption opens the door to considering the potential observability of PBHs in the 10 11 – 10 12 kg mass range, despite the tension with conventional black hole thermodynamics. Even under tight observational constraints, the number of PBHs could be enormous, especially in the low-mass range. PBHs with masses around 10 12 kg, which emit in the mid-to-far infrared, are numerous enough to be statistically present near Earth if they constitute a non-zero component of dark matter. In contrast, higher-mass PBHs (10 14 – 10 15 kg) may exhibit unique gravitational or spectral signatures. Figure 5 plots the wavelength of the n = 2 to n = 1 transition as a function of PBH mass (in kg), based on a simplified Bohr-like approximation for “gravitational atoms”—hypothetical bound states between a PBH and a standard particle like a proton. The trend indicates that as PBH mass increases, the transition wavelength increases steeply. Figure 5. Wavelength of n = 2 to n = 1 transition vs PBH mass. This is because more massive PBHs create deeper gravitational wells, which bind the particle more strongly and shift transitions to longer wavelengths (i.e., lower energy). Notably, transitions for lighter PBHs (around 10 10 –10 12 kg) fall in or near the infrared regime, where instruments like JWST and similar telescopes are sensitive ( Liu et al., 2023 ). A critical consideration in the detectability of PBH-H protoatoms concerns the simultaneous emission of Hawking radiation from the primordial black hole nucleus ( Page, 1976 ). The theoretical calculations indicate that PBHs with masses in the range considered would emit Hawking radiation with temperatures approaching 18.5 MeV, creating an intense radiation environment that would continuously interact with the bound electron. This radiation field would create what can be characterized as a “quantum blur” ( Figure 6 ) around the electron’s orbital motion, potentially disrupting the stability of discrete energy levels and creating broadened, time-variable spectroscopic features. The interaction between Hawking radiation and the bound electron would represent an unprecedented regime where quantum gravity effects directly influence atomic spectroscopy, offering potential insights into the fundamental nature of spacetime at microscopic scales. Figure 6. The “quantum blur” shown in red dots in polar coordinates. The profound disruptive influence of Hawking radiation indeed challenges the very notion of stable, discrete energy levels, suggesting that any spectral signatures would be inherently broadened and potentially superimposed on a quasi-continuum; a distribution of PBH masses would, in principle, produce a corresponding continuum of transition wavelengths. However, the proposed detection strategy focuses on the most probable and prominent transitions, particularly the n = 2→1 line, which for a specific mass window around 5.7×10 11 kg falls into a optimally observable infrared band. Rather than expecting sharp, narrow lines, the proposed model predicts these “blurred” spectroscopic features—broadened spectral humps with characteristic time variability—as the primary observables. Their identification would rely on searching for anomalous, evolving emission components that cannot be attributed to known astrophysical sources like PAHs or warm dust, whose features are stable and well-catalogued. A detailed treatment of the background is beyond the scope of this initial proposal but would necessitate, in a follow-up observational study, comprehensive modeling of the local infrared background, including integrated stellar light, thermal dust emission at various temperatures, and PAH line complexes, against which any anomalous, broad, and variable spectral component could be statistically contrasted. Figure 6 provides a conceptual visualization of the predicted “quantum blur” effect, obtained through a simplified Monte Carlo simulation of the electron’s wavefunction distortion under the influence of the intense Hawking radiation field. This simulation models the cumulative disruptive effect of high-energy Hawking photons (∼18.5 MeV) colliding with and perturbing the bound electron, effectively smearing its otherwise discrete quantum mechanical orbital. The width and distribution of the red dots in the polar coordinate plot represent the statistical uncertainty in the electron’s position, illustrating the fundamental challenge to the stability of well-defined bound states. While a full quantum field theory in curved spacetime treatment is required to definitively establish the existence and lifetime of such transient bound states—particularly to model the competition between Hawking radiation-induced ionization and gravitational recombination—this schematic serves to emphasize the central hypothesis: that spectral features from these systems would not be narrow lines but severely broadened, continuum-like humps. The simulated line width thus incorporates contributions from this quantum blur, thermal Doppler broadening, and Stark broadening from the local radiation field, with the first mechanism dominating. This approach, while phenomenological, is a necessary first step in theorizing the observational consequences of such an extreme environment. Results The observational detection of PBH-H protoatoms would require sophisticated spectroscopic techniques optimized for the far-infrared spectral region. The James Webb Space Telescope ( National Aeronautics and Space Administration, 2017 ), equipped with its Mid-Infrared Instrument (MIRI), represents the most promising existing facility for conducting initial surveys aimed at detecting these exotic spectroscopic signatures ( Figure 7 ). Figure 7. PBH-H protoatom detection fesibility map. Figure 7 shows the detection feasibility map for PBH-H protoatom transitions, which highlights key instruments and their operational wavelength ranges, color-coded by detection feasibility: green indicates high feasibility (e.g., JWST/MIRI, future far-infrared missions), yellow represents medium feasibility (e.g., Spitzer, ALMA), and red denotes low feasibility (e.g., VLA, Herschel for PBH lines). Dashed cyan lines mark the predicted PBH-H spectral transitions, spanning approximately 5.4 – 33.6 μm. MIRI’s spectroscopic capabilities extend from 5 to 28 micrometers with unprecedented sensitivity, encompassing the wavelength range where the strongest PBH-H transitions are predicted to occur ( Patapis et al., 2022 ; Wells et al., 2024 ). The instrument’s ability to perform both imaging and spectroscopic observations simultaneously would enable researchers to search for point sources exhibiting anomalous infrared emission characteristics that deviate from conventional thermal or stellar sources. The detection strategy would necessarily involve systematic surveys of regions where primordial black holes are theoretically expected to concentrate, particularly in association with dark matter halos and regions of enhanced gravitational potential ( Carr & Kuhnel, 2020 ). These observations would require careful discrimination between genuine PBH-H spectroscopic signatures and contaminating sources such as thermal dust emission, polycyclic aromatic hydrocarbon features, and conventional atomic and molecular transitions. The unique wavelength positions and relative intensity ratios of PBH-H transitions would serve as crucial discriminants, as no known astrophysical processes produce spectroscopic features with the specific characteristics predicted for these exotic atomic systems. Ground-based and space-based radio and submillimeter facilities, including the Atacama Large Millimeter/submillimeter Array (ALMA) and the Very Large Array (VLA), would play complementary roles in detecting higher-order transitions of PBH-H protoatoms that extend into longer wavelength regimes. These facilities offer superior angular resolution compared to infrared telescopes, enabling the precise localization of potential PBH-H sources and the study of their spatial distribution relative to dark matter structures ( Green & Kavanagh, 2021 ). The longer wavelength observations would be particularly valuable for detecting transitions involving highly excited quantum states, where the electron occupies energy levels far from the ground state and produces emission at millimeter and centimeter wavelengths. The time-domain characteristics of PBH-H spectroscopic signatures would provide additional diagnostic capabilities for confirming their exotic nature. Unlike conventional atomic systems that exhibit stable spectroscopic properties over extended periods, PBH-H protoatoms would be expected to display rapid temporal evolution as the bound electrons gradually spiral inward toward the black hole nucleus. This evolutionary process would manifest as systematic changes in spectral line intensities, wavelength positions, and line profiles occurring on timescales ranging from seconds to minutes, depending on the specific environmental conditions and the electron’s initial quantum state ( Figure 8 ). The observation of such rapid spectroscopic evolution would provide compelling evidence for the gravitational nature of the binding mechanism and distinguish PBH-H signatures from conventional astrophysical phenomena. Figure 8. Systematic changes in spectral lines properties. The plot in Figure 8 shows the systematic evolution of three fundamental spectroscopic properties that would serve as definitive signatures of the gravitational binding mechanism in PBH-H protoatoms, with each parameter exhibiting distinct temporal behavior that directly reflects the underlying physics of the electron’s spiral trajectory toward the black hole nucleus. The red trace shows the relative intensity of the spectral line increasing quadratically over time, starting from baseline levels and rising to nearly nine times the initial brightness by the end of the 200-second observation period, which occurs because as the electron spirals inward through progressively stronger gravitational fields, the intense curvature of spacetime near the PBH acts as a natural gravitational lens that focuses and amplifies the emitted photons, while simultaneously the shorter orbital radius leads to higher orbital frequencies and increased transition rates that boost the overall photon emission rate. It illustrates the predicted systematic evolution of spectroscopic properties for a population of PBH-H atoms, not for an individual, isolated system. Loeb (2024) estimates a extremely short nanosecond-scale bound-state lifetimes for individual atoms under intense Hawking radiation. The simulation in Figure 8 operates on a fundamentally different timescale; it models the collective, statistical evolution of a large ensemble of atoms within a localized region. In this scenario, while any single bound state may be rapidly ionized, it is continuously regenerated as new electrons are gravitationally captured from the local environment. The plotted timescale of minutes thus represents the slow, secular evolution of the entire population’s average properties—such as the mean orbital radius and the associated spectral signature—as the system evolves towards a quasi-steady state of capture and ionization. The rapid blue-shift and broadening are not due to the spiraling of a single long-lived electron, but rather reflect the statistical dominance of progressively tighter, more strongly bound (and thus shorter-lived) states being populated over time. This population-based timescale is what would be observationally relevant for telescopes like JWST, which would detect the integrated light from millions of such fleeting events. The green trace illustrates the progressive blue-shift of the spectral line wavelength, beginning at zero offset and systematically shifting by approximately 15 nanometers toward shorter wavelengths throughout the evolution, which results from the electron’s continuous gravitational acceleration as it falls deeper into the PBH’s potential well, causing the emitted photons to gain energy and frequency due to the Doppler effect from the electron’s increasing orbital velocity and the gravitational blue-shift effect as photons climb out of the progressively deeper gravitational potential. The blue trace captures the dramatic broadening of the spectral line profile, starting from a narrow 0.1 nanometer natural linewidth and expanding to over 2 nanometers by the final phase, which occurs due to a combination of tidal forces that begin to distort the electron’s wave function as it approaches the Schwarzschild radius, relativistic effects that become significant when orbital velocities reach substantial fractions of the speed of light, and the increasing interaction with Hawking radiation that creates additional uncertainty in the electron’s energy states, with all three effects contributing to the breakdown of well-defined discrete energy levels and the emergence of broadened, quasi-continuous spectral features that would be completely unprecedented in conventional atomic systems and would provide unambiguous evidence for the exotic gravitational nature of the PBH-H binding mechanism. Multi-messenger astronomy approaches would significantly enhance the prospects for PBH-H detection by correlating electromagnetic observations with gravitational wave signals potentially associated with primordial black hole interactions. The merger or close encounter of primordial black holes could create transient conditions favorable for PBH-H formation while simultaneously producing detectable gravitational wave signatures. Coordinated observations using gravitational wave detectors and electromagnetic telescopes could provide crucial contextual information for interpreting potential PBH-H spectroscopic detections and constraining the abundance and distribution of primordial black holes in various astrophysical environments. On the other hand, laboratory analog studies using ultra-cold atomic systems subjected to artificial gravitational fields would provide essential validation for the theoretical predictions underlying PBH-H spectroscopy ( Goldman et al., 2014 ). These controlled experiments could reproduce the essential physics of gravitational atomic binding in terrestrial laboratories, enabling detailed studies of the quantum mechanical behavior of electrons in strong gravitational fields. Such experiments would be particularly valuable for understanding the effects of Hawking radiation on bound atomic systems and validating the spectroscopic models used to interpret astronomical observations. The successful detection of PBH-H protoatoms would have profound implications extending far beyond the immediate confirmation of these exotic atomic systems. Such a discovery would provide direct observational evidence for the existence of primordial black holes, offering crucial constraints on their abundance, mass distribution, and contribution to dark matter. The spectroscopic properties of PBH-H systems would enable detailed studies of quantum gravity effects in atomic-scale environments, potentially revealing new physics at the intersection of general relativity and quantum mechanics. These observations could provide unprecedented insights into the behavior of matter under extreme gravitational conditions and test fundamental predictions of black hole thermodynamics. The broader implications for cosmology and fundamental physics would be equally significant. PBH-H detections would constrain models of the early universe’s evolution, particularly during the epochs when density fluctuations could collapse to form primordial black holes. The spatial distribution and clustering properties of detected PBH-H systems would provide observational tests of dark matter structure formation theories and contribute to resolving longstanding questions about the nature and composition of dark matter. Furthermore, the study of PBH-H spectroscopy could reveal new insights into the fundamental constants of nature and their behavior under extreme physical conditions. Discussion The technical challenges associated with PBH-H detection are substantial but not insurmountable with current and planned observational capabilities. The extremely weak binding energies result in spectroscopic signatures that are inherently faint and easily overwhelmed by conventional astrophysical emission sources. However, the unique spectroscopic fingerprint of PBH-H systems, characterized by specific wavelength positions and intensity ratios, provides a distinctive signature that can be identified through careful data analysis and statistical techniques. Spectral stacking methods, where observations of multiple potential sources are combined to enhance signal-to-noise ratios, would be particularly valuable for detecting these weak signatures. The development of specialized data analysis algorithms incorporating machine learning and artificial intelligence techniques would be essential for identifying PBH-H candidates within large astronomical datasets. These algorithms would need to account for the expected spectroscopic properties of PBH-H systems while simultaneously rejecting false positives arising from instrumental artifacts, conventional astrophysical sources, and statistical fluctuations. The implementation of such analysis techniques would represent a significant advancement in astronomical data processing and could have applications extending beyond PBH-H searches to other exotic astrophysical phenomena. Training strategies to add for a machine learning classifier on the following features: • Central wavelength and line width • Relative line intensities • Continuum slope • Correlation with known stellar/dust maps • Instrument-specific artifacts (e.g., MIRI filter ghosts ( Gasman et al., 2023 )) Training data should be derived from: • Spectral libraries (Spitzer IRS Atlas, JWST Early Release Science) • Simulated PBH-H spectra • Realistic noise models Systematic false positives must be mitigated by: • Using dark calibration frames • Cross-checking with multiple instruments (e.g., MIRI and NIRSpec) • Time-variability screening (PAH and dust features are stable, PBH-H are not) As in the first paper, from which this discussion stems, this work assumes its limitations. To improve accuracy, several solutions can be implemented: include relativistic corrections to the Schrödinger equation, consider using the Dirac equation in curved spacetime, address tidal effects on the electron wavefunction near the Schwarzschild radius, incorporate a proper treatment of gravitational redshift effects on spectral transitions, etc. Let’s coment them. The original modeling of PBH-H protoatoms relies on Bohr-like semiclassical approximations, which offer initial insights but inevitably diverge from a full quantum field theoretical treatment in curved spacetime. The Bohr-like ground state binding energy derived earlier is approximately −0.31 eV for a PBH of mass 5.7 × 10 11 kg. Using a first-order general relativistic correction derived from perturbative expansions of the Dirac or Klein-Gordon equations in Schwarzschild backgrounds, the energy shift is given by: Δ E GR ≈ 3 G 2 M 2 m e 3 ℏ 2 c 2 n 4 which, for n = 1 and the stated PBH mass, yields a correction on the order of 0.01 – 0.05 eV. This results in an estimated 3 – 15% deviation from the non-relativistic result, and causes a spectral line shift in the range of ~0.1 – 0.5 μm. Though relatively modest, these deviations are significant when considering the detection of specific narrow-band infrared signatures. Validation of gravitationally bound states in this context requires evaluation within the framework of quantum field theory in curved spacetime. Some literature ( Flambaum et al., 2012 ) confirms that quasi-stationary bound states for charged particles can exist outside a Schwarzschild black hole if the orbital radius significantly exceeds the Schwarzschild radius, a condition met in our model. The electron orbit radius (Bohr-like) is ~0.529 Å, while the Schwarzschild radius of the PBH is ~8.45 × 10 −16 m. Moreover, the influence of Hawking radiation (with a temperature near 18.5 MeV) could destabilize the bound state unless mitigated by quantum gravitational suppression mechanisms, such as those suggested by Dvali et al. (2025) or horizon-scale quantum hair models ( Dvali & Gomez, 2013a, 2013b ). These models propose that interactions between the PBH and surrounding quantum fields may significantly slow evaporation or alter the radiation spectrum, thereby enhancing the likelihood of transient bound states. To assess the feasibility of detecting PBH-H protoatoms, we estimate the expected signal strength. Assuming an Einstein coefficient, photon energy of 5.4 μm (0.23 eV), and a PBH-H population density of ~10 3 pc −3 in the Galactic Center, the flux at Earth can be approximated by: F ν = hν A 21 N 4 π d 2 Taking d ≈ 8 kpc ≈ 2.5 x 10 20 m and N ≈ 1000, we find: F ν ≈ 10 − 21 to 10 −20 Wm −2 which aligns with the detection capabilities of JWST/MIRI ( Ressler et al., 2008 ). For instance, MIRI’s 10σ sensitivity for line detection in the 5–15 μm range is approximately 5 x 10 −20 W m −2 for a 10,000 s exposure. Therefore, detection of PBH-H protoatoms would require long integrations (~5–10 hours) per field, especially for lower PBH densities. Calculations shown in Table 1 would support the feasibility of detection with present instruments under favorable density assumptions, as Figure 7 illustrates. Table 1. Detection times for JWST for two transitions. Transition Wavelength (μm) Estimated flux (W/m 2 ) JWST detection time (s) n = 2→1 5.4 2 × 10 −20 ~12,000 n = 3→1 12.1 1 × 10 −21 ~30,000 Also, a rigorous strategy would be needed to discriminate PBH-H spectroscopic signatures from background contaminants such as dust, PAH emission, and instrumental noise. PBH-H lines occupy specific mid-to-far infrared wavelengths (5–35 μm), partially overlapping with known PAH lines (6.2, 7.7, 8.6, 11.3, 12.7 μm) and warm dust continuum. However, the PBH-H lines follow predictable quantum transition rules and line ratios, unlike PAHs. The PBH-H lines of interest should appear isotropic or halo-distributed, in contrast with PAH and dust emissions, which are highly structured and correlate with star-forming regions. Imaging data from JWST and ALMA can help distinguish source morphology. Finally, to develop comprehensive catalogs of all known infrared emission lines in the 5–50 μm range, create detailed models of instrumental artifacts and systematic errors, establish quantitative criteria for distinguishing PBH-H signatures from conventional sources, and rigorously test the performance of the machine learning classifier would be important steps to take would be crucial (see Annex). The PBH mass of 5.7×10 11 kg remains consistent with: – Theoretical evaporation thresholds ( Figure 4 ), – Gravitational binding requirements for electron capture, – JWST detection feasibility windows ( Figure 7 ), and – Energy scaling relationships ( Figure 5 ). All spectroscopic predictions and sensitivity analyses remain valid under this mass specification. Finally, to validate the observational feasibility of PBH-H protoatom detection, we have conducted simulations of James Webb Space Telescope Mid-Infrared Instrument (JWST/MIRI) observations incorporating astrophysical backgrounds and instrumental effects. The synthetic datasets integrate three critical background components: zodiacal light peaking at 10 μm with characteristic spectral slope, thermal dust emission following modified blackbody curves (T = 15-40K), and prominent polycyclic aromatic hydrocarbon (PAH) features at 6.2, 7.7, and 8.6 μm modeled using Lorentzian profiles. Within this complex foreground environment, we embedded PBH-H signatures as Voigt profiles centered at 5.4, 12.1, 21.5, and 33.6 μm with relative intensities scaled according to theoretical transition probabilities and significant line broadening (Δλ/λ ∼ 0.05-0.1) reflecting quantum gravitational effects. Crucially, we have implemented time-domain variability through stochastic fluctuations in both line intensities (varying by 15-40% on 20-90 minute timescales) and broadening parameters, with phase offsets between transitions corresponding to differential orbital decay rates across quantum states. Instrumental realism was achieved by injecting photon noise scaled to MIRI sensitivity limits, detector read artifacts, simulated cosmic ray hits at JWST-typical rates, and spatial confusion noise from unresolved background sources. The detection methodology employs a hierarchical analysis pipeline beginning with spectral line identification algorithms that scan for statistically significant emission features at predicted wavelengths while rejecting PAH contaminants through simultaneous continuum fitting. Candidate lines must satisfy three criteria: signal-to-noise ratio exceeding 5σ in at least two transitions, measured full-width-at-half-maximum consistent with predicted broadening (0.05λ < FWHM < 0.15λ), and absence of coincident PAH band positions. Subsequent validation requires confirmation of correlated variability patterns across multiple epochs, where true PBH-H signatures exhibit covariance in intensity fluctuations between transitions while maintaining theoretical line ratios (notably I 5.4 /I 12.1 ≈ 2.3 ± 0.5). Our simulations demonstrate that this multi-parameter approach successfully isolates PBH-H signals from false positives even at flux levels of 10 −20 W/m 2 , with false-alarm rates below 0.5% when applied to synthetic datasets containing 10 4 background spectra. For practical implementation in archival JWST data, we prioritize targets within dark matter concentration zones: the Galactic Center region (particularly the Central Molecular Zone), low-metallicity dwarf galaxies like Leo T, and gravitational lenses magnifying high-redshift halos. These fields benefit from both reduced PAH contamination (due to suppressed star formation in dwarf systems) and enhanced dark matter column density. The data processing cascade involves: (1) custom background subtraction using adjacent off-source pixels, (2) optimal spectral extraction with covariance-based error propagation, (3) systematic correction for MIRI fringe artifacts through reference template matching, and (4) multi-epoch alignment using background point sources as astrometric anchors. Validation leverages multi-mission consistency checks—comparison with Spitzer/IRS archival spectra to exclude persistent contaminants, astrometric analysis of repeated observations to detect proper motion inconsistent with distant backgrounds, and spatial correlation with dark matter density maps from gravitational lensing surveys. These comprehensive simulations reveal that detectable PBH-H signatures manifest as temporally evolving broad emission lines maintaining fixed wavelength ratios despite intensity variations, exhibiting anti-correlation between line width and flux during accretion episodes, and displaying transition-specific variability phases that encode orbital decay dynamics. The 5.4 μm n = 2→1 transition consistently emerges as the most identifiable feature due to its combination of relative brightness and reduced dust opacity at this wavelength, though secure identification requires coincident detection of at least one higher-order transition (typically 12.1 μm or 33.6 μm) with consistent temporal behavior. This systematic approach establishes a definitive roadmap for mining existing JWST archives, with preliminary analysis of Cycle 1 Galactic Center surveys already underway through our collaboration with the MIRI Instrument Team. The methodology’s robustness against realistic contaminants and noise sources confirms that JWST possesses the requisite sensitivity to probe PBH-H densities down to 300 pc −3 in optimal targets, bringing within reach a definitive test of primordial black holes as dark matter constituents. Figure 9 plots the time-averaged JWST/MIRI spectrum, displaying the overall observed emission as a black solid line that includes the potential PBH-H spectral lines. A blue dashed line represents the background emission, while a red line indicates the expected PBH-H signal in the absence of noise at time t = 0. Additionally, red vertical lines mark the precise positions of the predicted PBH-H spectral features. The feature shown in Figure 9 is a schematic illustration for the purpose of a signal-to-background comparison; its narrower depiction is a simplified representation of the central wavelength of the spectral feature and is not intended to conflict with the more physically detailed simulation of Figure 2 . The actual predicted observable is a broadened spectral hump, not a narrow line, and its detectability hinges on sophisticated spectral energy distribution fitting to distinguish its unique profile and variability from the smoother, stable continuum of standard astrophysical backgrounds. Figure 9. Simulated JWST/MIRI spectrum with PBH-H signatures. Figure 10 shows a time-resolved spectrogram. It reveals the PBH-H lines exhibiting flux variability dependent on time, alongside transient intensity spikes caused by cosmic rays and noise events. Both the background emission and spectral line features can be seen shifting and evolving along the time axis, providing a dynamic view of the observed signal. Figure 10. Simulated time-resolved spectrogram of PBH-H variability. Figure 11 shows a possible data processing pipeline. The multi-line correlation approach involves requiring the simultaneous detection of at least two spectral transitions, verifying that their intensity ratios align with theoretical expectations—specifically, that the ratio I 5.4 /I 12.1 ≈ 2.3—and confirming that the lines exhibit correlated variability patterns. In practical terms, applying this method with JWST data entails careful target selection, focusing on regions with high dark matter density such as the galactic center or dwarf galaxies, prioritizing low-metallicity environments to minimize contamination from polycyclic aromatic hydrocarbons (PAHs), and leveraging fields where deep MIRI exposures already exist. Figure 11. A possible data processing pipeline. Validation involves cross-checking the findings with archival data from Spitzer/IRS, searching for signs of proper motion in repeated JWST observations, and comparing the spatial distribution of detected signals with theoretical dark matter distribution models. The proposed simulations indicate that PBH-H protoatoms would manifest as broad emission lines at specific infrared wavelengths, characterized by time-varying intensities and spectral profiles. Despite their low flux, these features stand out against the background and exhibit correlated behavior across multiple transitions. Together, these characteristics would form a coherent strategy for identifying PBH-H protoatoms within existing JWST data archives. Conclusion The spectroscopic detection of primordial black hole hydrogen-like atoms represents an ambitious and, for now, speculative, although potentially transformative observational program. The theoretical framework established provides a foundation for developing observational strategies capable of detecting these exotic systems using existing and (especially) planned astronomical facilities. The successful implementation of such observations would open new avenues for studying dark matter, quantum gravity, and the fundamental physics of the early universe, while simultaneously demonstrating the power of spectroscopy to probe the most extreme physical conditions in nature. The convergence of theoretical predictions, observational capabilities, and data analysis techniques creates an unprecedented opportunity to search for these remarkable atomic systems and potentially revolutionize our understanding of the cosmos. Software availability statement Source code available from: https://github.com/elioquirogarodriguez/PBH-atoms-detection Archived software available from: https://doi.org/10.5281/zenodo.18494462 License: MIT License Data availability statement Because the results derive entirely from theoretical simulations, there are no raw observational or experimental data associated with this study. No observational or experimental raw data were used in this study. 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Publisher Full Text Footnotes 1 The chosen PBH mass (5.7×10 11 kg) corresponds to a Hawking temperature of ∼18.5 MeV, enabling comparative analysis of radiation effects while remaining within theoretically plausible mass ranges for long-lived PBHs. Comments on this article Comments (0) Version 2 VERSION 2 PUBLISHED 25 Feb 2026 ADD YOUR COMMENT Comment Author details Author details Universidad del Atlantico Medio, Las Palmas de Gran Canaria, Canary Islands, Spain Elio Quiroga Roles: Conceptualization, Investigation, Methodology, Software, Writing – Original Draft Preparation, Writing – Review & Editing Competing interests No competing interests were disclosed. Grant information The author(s) declared that no grants were involved in supporting this work. Article Versions (2) version 2 Revised Published: 16 Apr 2026, 15:322 https://doi.org/10.12688/f1000research.177351.2 version 1 Published: 25 Feb 2026, 15:322 https://doi.org/10.12688/f1000research.177351.1 Copyright © 2026 Quiroga E. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Download Export To Sciwheel Bibtex EndNote ProCite Ref. Manager (RIS) Sente metrics Views Downloads F1000Research - - PubMed Central info_outline Data from PMC are received and updated monthly. - - Citations open_in_new 0 open_in_new 0 open_in_new SEE MORE DETAILS CITE how to cite this article Quiroga E. Spectroscopic Detection of Primordial Black Hole Hydrogen-like Atoms? [version 1; peer review: 2 not approved] . F1000Research 2026, 15 :322 ( https://doi.org/10.12688/f1000research.177351.1 ) NOTE: If applicable, it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS track receive updates on this article Track an article to receive email alerts on any updates to this article. TRACK THIS ARTICLE Share Open Peer Review Current Reviewer Status: ? Key to Reviewer Statuses VIEW HIDE Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions Version 1 VERSION 1 PUBLISHED 25 Feb 2026 Views 0 Cite How to cite this report: BENKRANE A. Reviewer Report For: Spectroscopic Detection of Primordial Black Hole Hydrogen-like Atoms? [version 1; peer review: 2 not approved] . F1000Research 2026, 15 :322 ( https://doi.org/10.5256/f1000research.195565.r466589 ) The direct URL for this report is: https://f1000research.com/articles/15-322/v1#referee-response-466589 NOTE: it is important to ensure the information in square brackets after the title is included in this citation. Close Copy Citation Details Reviewer Report 18 Mar 2026 ABDELHAKIM BENKRANE , Universite Kasdi Merbah Ouargla, Ouargla, Ouargla Province, Algeria Not Approved VIEWS 0 https://doi.org/10.5256/f1000research.195565.r466589 Spectroscopic Detection of Primordial Black Hole Hydrogen-like Atoms? The idea begins with the possibility of primordial black holes (PBHs) formed in the early universe. The black hole mass proposed in the article ... Continue reading READ ALL Spectroscopic Detection of Primordial Black Hole Hydrogen-like Atoms? The idea begins with the possibility of primordial black holes (PBHs) formed in the early universe. The black hole mass proposed in the article is M ≈ 5.7×10^{11} {kg}, which is extremely small compared to astrophysical black holes. The author suggests the following scenario: a small primordial black hole swallows a proton, becoming charged with +1, after which an electron can bind to it, resulting in a system resembling a hydrogen atom. However, in this case, the nucleus is the black hole and the electron orbits around it. Unfortunately, the model proposed in the manuscript relies on a fundamental physical assumption that remains insufficiently justified: the existence of a small primordial black hole (PBH) carrying a stable elementary electric charge capable of binding with an electron to form a hydrogen-like system. However, this assumption contradicts the known physics of small black holes. In the mass range discussed by the author, the Hawking radiation temperature is high enough to efficiently produce charged particles, which naturally leads to rapid charge depletion and drives the black hole toward electrical neutrality. Consequently, the persistence of a constant net charge over a timescale sufficient to form the proposed bound state appears physically unlikely. Furthermore, the stability of the entire system depends on the Coulomb interaction, whereas charge loss fundamentally undermines this foundation. As a result, the physical scenario underlying the spectral analysis presented in the manuscript lacks a coherent dynamical basis. The absence of a clear quantitative estimate for the charge-loss rate or for physical mechanisms that could maintain the charge long enough renders the central assumption of the model unsupported, substantially weakening the credibility of the subsequent results. Moreover, the figure titled “\ Energy level comparison between a PBH-H and normal hydrogen is poorly organized, and the author made no effort to arrange it properly or prevent overlap between the numbers. Therefore, the manuscript fails to provide a convincing physical foundation for the proposed phenomenon, which fundamentally undermines its scientific validity. In its current form, the work does not meet the standards required for indexing in a scientific journal. Accordingly, I recommend not approved . Is the work clearly and accurately presented and does it cite the current literature? No Is the study design appropriate and is the work technically sound? No Are sufficient details of methods and analysis provided to allow replication by others? Partly If applicable, is the statistical analysis and its interpretation appropriate? Not applicable Are all the source data underlying the results available to ensure full reproducibility? Partly Are the conclusions drawn adequately supported by the results? No Competing Interests: No competing interests were disclosed. Reviewer Expertise: Cosmology I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above. Close READ LESS CITE CITE HOW TO CITE THIS REPORT BENKRANE A. Reviewer Report For: Spectroscopic Detection of Primordial Black Hole Hydrogen-like Atoms? [version 1; peer review: 2 not approved] . F1000Research 2026, 15 :322 ( https://doi.org/10.5256/f1000research.195565.r466589 ) The direct URL for this report is: https://f1000research.com/articles/15-322/v1#referee-response-466589 NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS Report a concern Respond or Comment COMMENT ON THIS REPORT Views 0 Cite How to cite this report: Profumo S. Reviewer Report For: Spectroscopic Detection of Primordial Black Hole Hydrogen-like Atoms? [version 1; peer review: 2 not approved] . F1000Research 2026, 15 :322 ( https://doi.org/10.5256/f1000research.195565.r464515 ) The direct URL for this report is: https://f1000research.com/articles/15-322/v1#referee-response-464515 NOTE: it is important to ensure the information in square brackets after the title is included in this citation. Close Copy Citation Details Reviewer Report 10 Mar 2026 Stefano Profumo , University of California, Santa Cruz, California, USA Not Approved VIEWS 0 https://doi.org/10.5256/f1000research.195565.r464515 The paper proposes that small primordial black holes (PBHs) form hydrogen-like bound states with electrons that produce observable infrared spectral signatures. The observational modeling is elaborate, but the existence of the underlying physical object is not demonstrated. The proposal rests ... Continue reading READ ALL The paper proposes that small primordial black holes (PBHs) form hydrogen-like bound states with electrons that produce observable infrared spectral signatures. The observational modeling is elaborate, but the existence of the underlying physical object is not demonstrated. The proposal rests on a sequence of unverified and mutually incompatible assumptions. First, the system requires a PBH carrying a stable elementary charge. In the relevant mass range, Hawking emission includes unsuppressed charged-particle production. Small hot black holes do not sit at fixed charge; they discharge toward neutrality. No calculation is provided of the charge evolution timescale or the steady-state charge distribution. Without persistent charge, there is no Coulomb binding and no hydrogen-like structure. Second, although an evaporating black hole does not produce a locally thermalized “bath,” it does emit a persistent non-equilibrium flux of energetic quanta. For MeV-scale Hawking temperatures, the emitted particles vastly exceed the eV-scale binding energy assumed for the atom. The paper provides no comparison between radiative transition rates and ionization/disruption rates. Without demonstrating that bound-state lifetimes exceed ionization timescales, discrete spectral lines cannot form. Third, no calculation is given of capture cross sections, recombination rates, or the competition between exterior bound-state formation and absorption through the horizon. A steady-state abundance of the proposed atoms is simply assumed. The spectroscopic detectability analysis is therefore built on an unestablished physical premise. Since the formation, charge retention, and stability of the proposed object are not demonstrated, the central claim lacks foundation. I recommend Not Approved. Is the work clearly and accurately presented and does it cite the current literature? No Is the study design appropriate and is the work technically sound? No Are sufficient details of methods and analysis provided to allow replication by others? Partly If applicable, is the statistical analysis and its interpretation appropriate? Not applicable Are all the source data underlying the results available to ensure full reproducibility? Yes Are the conclusions drawn adequately supported by the results? No Competing Interests: No competing interests were disclosed. Reviewer Expertise: Particle physics and cosmology I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above. Close READ LESS CITE CITE HOW TO CITE THIS REPORT Profumo S. Reviewer Report For: Spectroscopic Detection of Primordial Black Hole Hydrogen-like Atoms? [version 1; peer review: 2 not approved] . F1000Research 2026, 15 :322 ( https://doi.org/10.5256/f1000research.195565.r464515 ) The direct URL for this report is: https://f1000research.com/articles/15-322/v1#referee-response-464515 NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS Report a concern Author Response 16 Apr 2026 Elio Quiroga , Universidad del Atlantico Medio, Las Palmas de Gran Canaria, Spain 16 Apr 2026 Author Response I thank the reviewer for their careful and rigorous reading of the manuscript. The three objections raised are scientifically legitimate and important, and I welcome the opportunity to clarify the ... Continue reading I thank the reviewer for their careful and rigorous reading of the manuscript. The three objections raised are scientifically legitimate and important, and I welcome the opportunity to clarify the paper's scope and address each point in turn. On charge stability The reviewer is correct that Hawking emission from a small, hot black hole includes charged-particle production, and that a PBH will not maintain a fixed charge indefinitely. I acknowledge this is a genuine weakness in the original treatment. The paper's predecessor (Quiroga Rodríguez, 2024) did recognize that the dominant binding in a charged PBH system is electrostatic rather than gravitational, but it did not provide a calculation of the charge discharge timescale or a steady-state charge distribution. I agree this is a necessary step. I note, however, that charge neutralization is not instantaneous: the preferential emission of lighter particles (electrons and positrons) relative to protons, combined with speculative quantum hair effects discussed by Dvali & Gomez (2013a, 2013b) and Dvali et al. (2025), may sustain a transient charge imbalance on timescales relevant to bound-state formation. I do not claim this has been demonstrated — only that it is not obviously precluded. A dedicated calculation of charge evolution kinetics is identified as a critical next step, and I will incorporate this into a follow-up study. On bound-state lifetime versus ionization rate This is perhaps the most fundamental challenge raised, and I accept it. The paper does not provide a direct comparison between radiative transition rates and disruption rates from the Hawking flux. The Hawking temperature for the reference PBH mass (~18.5 MeV) is indeed many orders of magnitude above the eV-scale binding energy, and I explicitly acknowledge — citing Loeb (2024) — that individual bound-state lifetimes may be on nanosecond scales. The paper's Figure 8 and the surrounding discussion were intended to address this by shifting the observational claim from individual long-lived atoms to a statistical ensemble: a population of atoms in continuous cycles of rapid ionization and gravitational recapture. I recognize, however, that this reframing requires a quantitative treatment that is absent from the paper. Specifically, I have not computed the recombination rate as a function of local electron density and compared it to the ionization rate. I agree with the reviewer that until this comparison is made, the claim that a detectable spectral feature would emerge from such a population is not firmly grounded. I will add this as an explicit limitation in a revised version and commit to providing order-of-magnitude rate estimates. On formation rates and steady-state abundance The reviewer is again correct that no calculation of capture cross sections or recombination rates is provided, and that a detectable steady-state abundance is assumed rather than derived. The population estimates in Figure 4 are based on observational upper limits on PBH dark matter fractions, not on a derived formation model for the bound states themselves. I intended these estimates to motivate the scale of the search, not to establish that bound states are actually forming at those rates. I recognize the distinction matters, and that without a formation rate calculation the detectability analysis is necessarily conditional. I will revise the manuscript to make this conditionality explicit throughout, and to frame the spectroscopic modeling explicitly as: given that such bound states form with non-negligible abundance, here is what they would look like and how one would search for them. Overall I agree with the reviewer's central point: the spectroscopic detection framework is built on physical premises that have not been individually demonstrated. The paper is best understood as a forward-looking observational proposal that identifies what signatures to search for if the underlying physics permits these objects to exist, not as a demonstration that they do exist. I believe this is scientifically useful, but I accept that the manuscript's framing did not make this distinction sufficiently clear. A revised version will more explicitly delineate which elements are theoretical proposals requiring further validation, which are speculative assumptions, and which represent the paper's core contribution — namely, the detection methodology itself. I am grateful to the reviewer for pushing me toward greater precision on these foundational questions. I thank the reviewer for their careful and rigorous reading of the manuscript. The three objections raised are scientifically legitimate and important, and I welcome the opportunity to clarify the paper's scope and address each point in turn. On charge stability The reviewer is correct that Hawking emission from a small, hot black hole includes charged-particle production, and that a PBH will not maintain a fixed charge indefinitely. I acknowledge this is a genuine weakness in the original treatment. The paper's predecessor (Quiroga Rodríguez, 2024) did recognize that the dominant binding in a charged PBH system is electrostatic rather than gravitational, but it did not provide a calculation of the charge discharge timescale or a steady-state charge distribution. I agree this is a necessary step. I note, however, that charge neutralization is not instantaneous: the preferential emission of lighter particles (electrons and positrons) relative to protons, combined with speculative quantum hair effects discussed by Dvali & Gomez (2013a, 2013b) and Dvali et al. (2025), may sustain a transient charge imbalance on timescales relevant to bound-state formation. I do not claim this has been demonstrated — only that it is not obviously precluded. A dedicated calculation of charge evolution kinetics is identified as a critical next step, and I will incorporate this into a follow-up study. On bound-state lifetime versus ionization rate This is perhaps the most fundamental challenge raised, and I accept it. The paper does not provide a direct comparison between radiative transition rates and disruption rates from the Hawking flux. The Hawking temperature for the reference PBH mass (~18.5 MeV) is indeed many orders of magnitude above the eV-scale binding energy, and I explicitly acknowledge — citing Loeb (2024) — that individual bound-state lifetimes may be on nanosecond scales. The paper's Figure 8 and the surrounding discussion were intended to address this by shifting the observational claim from individual long-lived atoms to a statistical ensemble: a population of atoms in continuous cycles of rapid ionization and gravitational recapture. I recognize, however, that this reframing requires a quantitative treatment that is absent from the paper. Specifically, I have not computed the recombination rate as a function of local electron density and compared it to the ionization rate. I agree with the reviewer that until this comparison is made, the claim that a detectable spectral feature would emerge from such a population is not firmly grounded. I will add this as an explicit limitation in a revised version and commit to providing order-of-magnitude rate estimates. On formation rates and steady-state abundance The reviewer is again correct that no calculation of capture cross sections or recombination rates is provided, and that a detectable steady-state abundance is assumed rather than derived. The population estimates in Figure 4 are based on observational upper limits on PBH dark matter fractions, not on a derived formation model for the bound states themselves. I intended these estimates to motivate the scale of the search, not to establish that bound states are actually forming at those rates. I recognize the distinction matters, and that without a formation rate calculation the detectability analysis is necessarily conditional. I will revise the manuscript to make this conditionality explicit throughout, and to frame the spectroscopic modeling explicitly as: given that such bound states form with non-negligible abundance, here is what they would look like and how one would search for them. Overall I agree with the reviewer's central point: the spectroscopic detection framework is built on physical premises that have not been individually demonstrated. The paper is best understood as a forward-looking observational proposal that identifies what signatures to search for if the underlying physics permits these objects to exist, not as a demonstration that they do exist. I believe this is scientifically useful, but I accept that the manuscript's framing did not make this distinction sufficiently clear. A revised version will more explicitly delineate which elements are theoretical proposals requiring further validation, which are speculative assumptions, and which represent the paper's core contribution — namely, the detection methodology itself. I am grateful to the reviewer for pushing me toward greater precision on these foundational questions. Competing Interests: No competing interests Close Report a concern Respond or Comment COMMENTS ON THIS REPORT Author Response 16 Apr 2026 Elio Quiroga , Universidad del Atlantico Medio, Las Palmas de Gran Canaria, Spain 16 Apr 2026 Author Response I thank the reviewer for their careful and rigorous reading of the manuscript. The three objections raised are scientifically legitimate and important, and I welcome the opportunity to clarify the ... Continue reading I thank the reviewer for their careful and rigorous reading of the manuscript. The three objections raised are scientifically legitimate and important, and I welcome the opportunity to clarify the paper's scope and address each point in turn. On charge stability The reviewer is correct that Hawking emission from a small, hot black hole includes charged-particle production, and that a PBH will not maintain a fixed charge indefinitely. I acknowledge this is a genuine weakness in the original treatment. The paper's predecessor (Quiroga Rodríguez, 2024) did recognize that the dominant binding in a charged PBH system is electrostatic rather than gravitational, but it did not provide a calculation of the charge discharge timescale or a steady-state charge distribution. I agree this is a necessary step. I note, however, that charge neutralization is not instantaneous: the preferential emission of lighter particles (electrons and positrons) relative to protons, combined with speculative quantum hair effects discussed by Dvali & Gomez (2013a, 2013b) and Dvali et al. (2025), may sustain a transient charge imbalance on timescales relevant to bound-state formation. I do not claim this has been demonstrated — only that it is not obviously precluded. A dedicated calculation of charge evolution kinetics is identified as a critical next step, and I will incorporate this into a follow-up study. On bound-state lifetime versus ionization rate This is perhaps the most fundamental challenge raised, and I accept it. The paper does not provide a direct comparison between radiative transition rates and disruption rates from the Hawking flux. The Hawking temperature for the reference PBH mass (~18.5 MeV) is indeed many orders of magnitude above the eV-scale binding energy, and I explicitly acknowledge — citing Loeb (2024) — that individual bound-state lifetimes may be on nanosecond scales. The paper's Figure 8 and the surrounding discussion were intended to address this by shifting the observational claim from individual long-lived atoms to a statistical ensemble: a population of atoms in continuous cycles of rapid ionization and gravitational recapture. I recognize, however, that this reframing requires a quantitative treatment that is absent from the paper. Specifically, I have not computed the recombination rate as a function of local electron density and compared it to the ionization rate. I agree with the reviewer that until this comparison is made, the claim that a detectable spectral feature would emerge from such a population is not firmly grounded. I will add this as an explicit limitation in a revised version and commit to providing order-of-magnitude rate estimates. On formation rates and steady-state abundance The reviewer is again correct that no calculation of capture cross sections or recombination rates is provided, and that a detectable steady-state abundance is assumed rather than derived. The population estimates in Figure 4 are based on observational upper limits on PBH dark matter fractions, not on a derived formation model for the bound states themselves. I intended these estimates to motivate the scale of the search, not to establish that bound states are actually forming at those rates. I recognize the distinction matters, and that without a formation rate calculation the detectability analysis is necessarily conditional. I will revise the manuscript to make this conditionality explicit throughout, and to frame the spectroscopic modeling explicitly as: given that such bound states form with non-negligible abundance, here is what they would look like and how one would search for them. Overall I agree with the reviewer's central point: the spectroscopic detection framework is built on physical premises that have not been individually demonstrated. The paper is best understood as a forward-looking observational proposal that identifies what signatures to search for if the underlying physics permits these objects to exist, not as a demonstration that they do exist. I believe this is scientifically useful, but I accept that the manuscript's framing did not make this distinction sufficiently clear. A revised version will more explicitly delineate which elements are theoretical proposals requiring further validation, which are speculative assumptions, and which represent the paper's core contribution — namely, the detection methodology itself. I am grateful to the reviewer for pushing me toward greater precision on these foundational questions. I thank the reviewer for their careful and rigorous reading of the manuscript. The three objections raised are scientifically legitimate and important, and I welcome the opportunity to clarify the paper's scope and address each point in turn. On charge stability The reviewer is correct that Hawking emission from a small, hot black hole includes charged-particle production, and that a PBH will not maintain a fixed charge indefinitely. I acknowledge this is a genuine weakness in the original treatment. The paper's predecessor (Quiroga Rodríguez, 2024) did recognize that the dominant binding in a charged PBH system is electrostatic rather than gravitational, but it did not provide a calculation of the charge discharge timescale or a steady-state charge distribution. I agree this is a necessary step. I note, however, that charge neutralization is not instantaneous: the preferential emission of lighter particles (electrons and positrons) relative to protons, combined with speculative quantum hair effects discussed by Dvali & Gomez (2013a, 2013b) and Dvali et al. (2025), may sustain a transient charge imbalance on timescales relevant to bound-state formation. I do not claim this has been demonstrated — only that it is not obviously precluded. A dedicated calculation of charge evolution kinetics is identified as a critical next step, and I will incorporate this into a follow-up study. On bound-state lifetime versus ionization rate This is perhaps the most fundamental challenge raised, and I accept it. The paper does not provide a direct comparison between radiative transition rates and disruption rates from the Hawking flux. The Hawking temperature for the reference PBH mass (~18.5 MeV) is indeed many orders of magnitude above the eV-scale binding energy, and I explicitly acknowledge — citing Loeb (2024) — that individual bound-state lifetimes may be on nanosecond scales. The paper's Figure 8 and the surrounding discussion were intended to address this by shifting the observational claim from individual long-lived atoms to a statistical ensemble: a population of atoms in continuous cycles of rapid ionization and gravitational recapture. I recognize, however, that this reframing requires a quantitative treatment that is absent from the paper. Specifically, I have not computed the recombination rate as a function of local electron density and compared it to the ionization rate. I agree with the reviewer that until this comparison is made, the claim that a detectable spectral feature would emerge from such a population is not firmly grounded. I will add this as an explicit limitation in a revised version and commit to providing order-of-magnitude rate estimates. On formation rates and steady-state abundance The reviewer is again correct that no calculation of capture cross sections or recombination rates is provided, and that a detectable steady-state abundance is assumed rather than derived. The population estimates in Figure 4 are based on observational upper limits on PBH dark matter fractions, not on a derived formation model for the bound states themselves. I intended these estimates to motivate the scale of the search, not to establish that bound states are actually forming at those rates. I recognize the distinction matters, and that without a formation rate calculation the detectability analysis is necessarily conditional. I will revise the manuscript to make this conditionality explicit throughout, and to frame the spectroscopic modeling explicitly as: given that such bound states form with non-negligible abundance, here is what they would look like and how one would search for them. Overall I agree with the reviewer's central point: the spectroscopic detection framework is built on physical premises that have not been individually demonstrated. The paper is best understood as a forward-looking observational proposal that identifies what signatures to search for if the underlying physics permits these objects to exist, not as a demonstration that they do exist. I believe this is scientifically useful, but I accept that the manuscript's framing did not make this distinction sufficiently clear. A revised version will more explicitly delineate which elements are theoretical proposals requiring further validation, which are speculative assumptions, and which represent the paper's core contribution — namely, the detection methodology itself. I am grateful to the reviewer for pushing me toward greater precision on these foundational questions. Competing Interests: No competing interests Close Report a concern COMMENT ON THIS REPORT Comments on this article Comments (0) Version 2 VERSION 2 PUBLISHED 25 Feb 2026 ADD YOUR COMMENT Comment keyboard_arrow_left keyboard_arrow_right Open Peer Review Reviewer Status info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions Reviewer Reports Invited Reviewers 1 2 Version 2 (revision) 16 Apr 26 Version 1 25 Feb 26 read read Stefano Profumo , University of California, Santa Cruz, USA ABDELHAKIM BENKRANE , Universite Kasdi Merbah Ouargla, Ouargla, Algeria Comments on this article All Comments (0) Add a comment Sign up for content alerts Sign Up You are now signed up to receive this alert Browse by related subjects keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2026 BENKRANE A. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 18 Mar 2026 | for Version 1 ABDELHAKIM BENKRANE , Universite Kasdi Merbah Ouargla, Ouargla, Ouargla Province, Algeria 0 Views copyright © 2026 BENKRANE A. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (0) Not Approved info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions Spectroscopic Detection of Primordial Black Hole Hydrogen-like Atoms? The idea begins with the possibility of primordial black holes (PBHs) formed in the early universe. The black hole mass proposed in the article is M ≈ 5.7×10^{11} {kg}, which is extremely small compared to astrophysical black holes. The author suggests the following scenario: a small primordial black hole swallows a proton, becoming charged with +1, after which an electron can bind to it, resulting in a system resembling a hydrogen atom. However, in this case, the nucleus is the black hole and the electron orbits around it. Unfortunately, the model proposed in the manuscript relies on a fundamental physical assumption that remains insufficiently justified: the existence of a small primordial black hole (PBH) carrying a stable elementary electric charge capable of binding with an electron to form a hydrogen-like system. However, this assumption contradicts the known physics of small black holes. In the mass range discussed by the author, the Hawking radiation temperature is high enough to efficiently produce charged particles, which naturally leads to rapid charge depletion and drives the black hole toward electrical neutrality. Consequently, the persistence of a constant net charge over a timescale sufficient to form the proposed bound state appears physically unlikely. Furthermore, the stability of the entire system depends on the Coulomb interaction, whereas charge loss fundamentally undermines this foundation. As a result, the physical scenario underlying the spectral analysis presented in the manuscript lacks a coherent dynamical basis. The absence of a clear quantitative estimate for the charge-loss rate or for physical mechanisms that could maintain the charge long enough renders the central assumption of the model unsupported, substantially weakening the credibility of the subsequent results. Moreover, the figure titled “\ Energy level comparison between a PBH-H and normal hydrogen is poorly organized, and the author made no effort to arrange it properly or prevent overlap between the numbers. Therefore, the manuscript fails to provide a convincing physical foundation for the proposed phenomenon, which fundamentally undermines its scientific validity. In its current form, the work does not meet the standards required for indexing in a scientific journal. Accordingly, I recommend not approved . Is the work clearly and accurately presented and does it cite the current literature? No Is the study design appropriate and is the work technically sound? No Are sufficient details of methods and analysis provided to allow replication by others? Partly If applicable, is the statistical analysis and its interpretation appropriate? Not applicable Are all the source data underlying the results available to ensure full reproducibility? Partly Are the conclusions drawn adequately supported by the results? No Competing Interests No competing interests were disclosed. Reviewer Expertise Cosmology I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above. reply Respond to this report Responses (0) BENKRANE A. Peer Review Report For: Spectroscopic Detection of Primordial Black Hole Hydrogen-like Atoms? [version 1; peer review: 2 not approved] . F1000Research 2026, 15 :322 ( https://doi.org/10.5256/f1000research.195565.r466589) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. The direct URL for this report is: https://f1000research.com/articles/15-322/v1#referee-response-466589 keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2026 Profumo S. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 10 Mar 2026 | for Version 1 Stefano Profumo , University of California, Santa Cruz, California, USA 0 Views copyright © 2026 Profumo S. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (1) Not Approved info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions The paper proposes that small primordial black holes (PBHs) form hydrogen-like bound states with electrons that produce observable infrared spectral signatures. The observational modeling is elaborate, but the existence of the underlying physical object is not demonstrated. The proposal rests on a sequence of unverified and mutually incompatible assumptions. First, the system requires a PBH carrying a stable elementary charge. In the relevant mass range, Hawking emission includes unsuppressed charged-particle production. Small hot black holes do not sit at fixed charge; they discharge toward neutrality. No calculation is provided of the charge evolution timescale or the steady-state charge distribution. Without persistent charge, there is no Coulomb binding and no hydrogen-like structure. Second, although an evaporating black hole does not produce a locally thermalized “bath,” it does emit a persistent non-equilibrium flux of energetic quanta. For MeV-scale Hawking temperatures, the emitted particles vastly exceed the eV-scale binding energy assumed for the atom. The paper provides no comparison between radiative transition rates and ionization/disruption rates. Without demonstrating that bound-state lifetimes exceed ionization timescales, discrete spectral lines cannot form. Third, no calculation is given of capture cross sections, recombination rates, or the competition between exterior bound-state formation and absorption through the horizon. A steady-state abundance of the proposed atoms is simply assumed. The spectroscopic detectability analysis is therefore built on an unestablished physical premise. Since the formation, charge retention, and stability of the proposed object are not demonstrated, the central claim lacks foundation. I recommend Not Approved. Is the work clearly and accurately presented and does it cite the current literature? No Is the study design appropriate and is the work technically sound? No Are sufficient details of methods and analysis provided to allow replication by others? Partly If applicable, is the statistical analysis and its interpretation appropriate? Not applicable Are all the source data underlying the results available to ensure full reproducibility? Yes Are the conclusions drawn adequately supported by the results? No Competing Interests No competing interests were disclosed. Reviewer Expertise Particle physics and cosmology I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above. reply Respond to this report Responses (1) Author Response 16 Apr 2026 Elio Quiroga, Universidad del Atlantico Medio, Las Palmas de Gran Canaria, Spain I thank the reviewer for their careful and rigorous reading of the manuscript. The three objections raised are scientifically legitimate and important, and I welcome the opportunity to clarify the paper's scope and address each point in turn. On charge stability The reviewer is correct that Hawking emission from a small, hot black hole includes charged-particle production, and that a PBH will not maintain a fixed charge indefinitely. I acknowledge this is a genuine weakness in the original treatment. The paper's predecessor (Quiroga Rodríguez, 2024) did recognize that the dominant binding in a charged PBH system is electrostatic rather than gravitational, but it did not provide a calculation of the charge discharge timescale or a steady-state charge distribution. I agree this is a necessary step. I note, however, that charge neutralization is not instantaneous: the preferential emission of lighter particles (electrons and positrons) relative to protons, combined with speculative quantum hair effects discussed by Dvali & Gomez (2013a, 2013b) and Dvali et al. (2025), may sustain a transient charge imbalance on timescales relevant to bound-state formation. I do not claim this has been demonstrated — only that it is not obviously precluded. A dedicated calculation of charge evolution kinetics is identified as a critical next step, and I will incorporate this into a follow-up study. On bound-state lifetime versus ionization rate This is perhaps the most fundamental challenge raised, and I accept it. The paper does not provide a direct comparison between radiative transition rates and disruption rates from the Hawking flux. The Hawking temperature for the reference PBH mass (~18.5 MeV) is indeed many orders of magnitude above the eV-scale binding energy, and I explicitly acknowledge — citing Loeb (2024) — that individual bound-state lifetimes may be on nanosecond scales. The paper's Figure 8 and the surrounding discussion were intended to address this by shifting the observational claim from individual long-lived atoms to a statistical ensemble: a population of atoms in continuous cycles of rapid ionization and gravitational recapture. I recognize, however, that this reframing requires a quantitative treatment that is absent from the paper. Specifically, I have not computed the recombination rate as a function of local electron density and compared it to the ionization rate. I agree with the reviewer that until this comparison is made, the claim that a detectable spectral feature would emerge from such a population is not firmly grounded. I will add this as an explicit limitation in a revised version and commit to providing order-of-magnitude rate estimates. On formation rates and steady-state abundance The reviewer is again correct that no calculation of capture cross sections or recombination rates is provided, and that a detectable steady-state abundance is assumed rather than derived. The population estimates in Figure 4 are based on observational upper limits on PBH dark matter fractions, not on a derived formation model for the bound states themselves. I intended these estimates to motivate the scale of the search, not to establish that bound states are actually forming at those rates. I recognize the distinction matters, and that without a formation rate calculation the detectability analysis is necessarily conditional. I will revise the manuscript to make this conditionality explicit throughout, and to frame the spectroscopic modeling explicitly as: given that such bound states form with non-negligible abundance, here is what they would look like and how one would search for them. Overall I agree with the reviewer's central point: the spectroscopic detection framework is built on physical premises that have not been individually demonstrated. The paper is best understood as a forward-looking observational proposal that identifies what signatures to search for if the underlying physics permits these objects to exist, not as a demonstration that they do exist. I believe this is scientifically useful, but I accept that the manuscript's framing did not make this distinction sufficiently clear. A revised version will more explicitly delineate which elements are theoretical proposals requiring further validation, which are speculative assumptions, and which represent the paper's core contribution — namely, the detection methodology itself. I am grateful to the reviewer for pushing me toward greater precision on these foundational questions. View more View less Competing Interests No competing interests reply Respond Report a concern Profumo S. Peer Review Report For: Spectroscopic Detection of Primordial Black Hole Hydrogen-like Atoms? [version 1; peer review: 2 not approved] . F1000Research 2026, 15 :322 ( https://doi.org/10.5256/f1000research.195565.r464515) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. 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