Bi-Structured Horizon Geometry and Spectral Dimension Running at Black Hole Horizons

Bi-Structured Horizon Geometry and Spectral Dimension Running at Black Hole Horizons | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 23 February 2026 V1 Latest version Share on Bi-Structured Horizon Geometry and Spectral Dimension Running at Black Hole Horizons Authors : Shalender Singh 0000-0003-3677-4043 [email protected] and Vishnu Priya Singh Parmar Authors Info & Affiliations https://doi.org/10.22541/au.177187058.85664775/v1 85 views 82 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract The black hole information paradox arises in part from an implicit identification: the metric structure governing spacetime geometry and the propagation structure governing quantum dynamics are assumed to coincide. We argue that relaxing this identification resolves the tension between the Equivalence Principle and unitarity without modifying either. Treating the event horizon as a bistructured space carrying an intrinsic metric geometry and an independent propagation graph, we show that the spectral dimension of the horizon is not a fixed invariant but a scale-dependent observable that runs from a reduced value at short times-identified with the scrambling regimeto the classical spacetime dimension at late times. This running is consistent with dimensional reduction phenomena established in causal dynamical triangulations, asymptotically safe gravity, and Hořava-Lifshitz gravity. In this framework, the AMPS firewall corresponds to the short-time spectral regime: a scale-dependent phase associated with constrained propagation, not a curvature singularity of the metric geometry. A freely falling observer probing the horizon at macroscopic timescales traverses the smooth metric structure and perceives no drama. Unitarity is preserved because the constrained propagation is generated by a Hermitian Laplacian. We present a lattice simulation demonstrating the spectral crossover explicitly, confirming the coexistence of a lowdimensional spectral trap and a smooth macroscopic geometry within a single object. Implications for gravitational wave echoes, holographic complexity, and Swampland-type consistency criteria are discussed. Supplementary Material File (event_horizon_geometry_v2.pdf) Download 736.86 KB Information & Authors Information Version history V1 Version 1 23 February 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords amps firewall bi-structured geometry black hole information paradox constrained laplacian dimensional reduction equivalence principle fast scrambling holographic complexity quantum graphs quantum gravity scrambling time Authors Affiliations Shalender Singh 0000-0003-3677-4043 [email protected] View all articles by this author Vishnu Priya Singh Parmar View all articles by this author Metrics & Citations Metrics Article Usage 85 views 82 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Shalender Singh, Vishnu Priya Singh Parmar. Bi-Structured Horizon Geometry and Spectral Dimension Running at Black Hole Horizons. Authorea . 23 February 2026. DOI: https://doi.org/10.22541/au.177187058.85664775/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. 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