Quantum Spectral Analysis of Non-Relativistic Particles in Schwarzschild Spacetime under the Aharonov–Bohm Effect and External Potentials

Quantum Spectral Analysis of Non-Relativistic Particles in Schwarzschild Spacetime under the Aharonov–Bohm Effect and External Potentials | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Quantum Spectral Analysis of Non-Relativistic Particles in Schwarzschild Spacetime under the Aharonov–Bohm Effect and External Potentials Ishaku Joshua Arewa, Moses Udoisoh, Salihu M. Aliyu, Obichukwu O. Obiajulu, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7103850/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study presents a semi-classical, non-relativistic quantum-mechanical analysis of bound-state spectra for a scalar particle in Schwarzschild spacetime, incorporating both external potentials and the Aharonov–Bohm (AB) effect. By reformulating the radial Schrödinger equation via the Rindler approximation and introducing the AB flux as a prescribed gauge potential, we derive analytical expressions for the energy eigenvalues under Coulomb and Mie-type confinement. The results reveal a rich interplay between spacetime curvature, topological phase contributions, and short-range potential structure. Specifically, increasing the Schwarzschild radius leads to a redshift and compression of energy levels, with curvature-induced terms eventually dominating the confinement landscape. The AB flux induces a tunable spectral shift through its modification of the effective angular momentum, though this effect remains secondary to gravitational curvature. The effective potential analysis illustrates how curvature and gauge phases combine to shape quantum bound states. While idealized, this model offers insights into the sensitivity of quantum spectra to geometry and topology, with potential relevance for analogue gravity experiments and synthetic gauge field simulations. The approach assumes a fixed background geometry and neglects backreaction and relativistic corrections, and the results should be interpreted within this approximate framework. These results find relevance in analog gravity systems, quantum simulations with synthetic gauge fields, and investigations of black hole-modified quantum systems. Schwarzschild Spacetime Particle Dynamics Black Hole Aharonov–Bohm Effect Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7103850","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":496420925,"identity":"762f5dcb-b500-480f-99ba-b06c704371b3","order_by":0,"name":"Ishaku Joshua Arewa","email":"","orcid":"","institution":"Taraba State University","correspondingAuthor":false,"prefix":"","firstName":"Ishaku","middleName":"Joshua","lastName":"Arewa","suffix":""},{"id":496420926,"identity":"41d31294-6a8c-4e6f-b0d4-f1cf129a6395","order_by":1,"name":"Moses Udoisoh","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCElEQVRIiWNgGAWjYBADxgZmBgZmhgoJCJeHeC1nSNICJJgZ2xgIa9Ftb3/48AfDYdl+dvaHjwvnWcgbHG9gfPC2jSFP3gG7FrMzZ4yNeRgOG89s5jE2nrlNwnDDmQPMhnPbGIoND+DQciOHTZqB4XDihsM8bNK82yQYN9xIADLaGBI3NuDSkv785w+wFvZn0rxzJOw33H/A/hu/lgQzoGdBWhjMpHkbJBI33GBgYwZpmY/D+yC/SPMYpEP8wnNMInnmmcRmyTnngHpxaTne/vDjjwpr2X7+4w8f89TU2fYdP3zww5sym8T5OBwGAQYoPHAcSTAYHMCnBSuQx2vLKBgFo2AUjCAAAC0RWnHUrJp6AAAAAElFTkSuQmCC","orcid":"","institution":"Ignatius Ajuru University of Education","correspondingAuthor":true,"prefix":"","firstName":"Moses","middleName":"","lastName":"Udoisoh","suffix":""},{"id":496420927,"identity":"2f73087a-98ad-4226-8184-f41565585d2c","order_by":2,"name":"Salihu M. 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By reformulating the radial Schr\u0026ouml;dinger equation via the Rindler approximation and introducing the AB flux as a prescribed gauge potential, we derive analytical expressions for the energy eigenvalues under Coulomb and Mie-type confinement. The results reveal a rich interplay between spacetime curvature, topological phase contributions, and short-range potential structure. Specifically, increasing the Schwarzschild radius leads to a redshift and compression of energy levels, with curvature-induced terms eventually dominating the confinement landscape. The AB flux induces a tunable spectral shift through its modification of the effective angular momentum, though this effect remains secondary to gravitational curvature. The effective potential analysis illustrates how curvature and gauge phases combine to shape quantum bound states. While idealized, this model offers insights into the sensitivity of quantum spectra to geometry and topology, with potential relevance for analogue gravity experiments and synthetic gauge field simulations. The approach assumes a fixed background geometry and neglects backreaction and relativistic corrections, and the results should be interpreted within this approximate framework. These results find relevance in analog gravity systems, quantum simulations with synthetic gauge fields, and investigations of black hole-modified quantum systems.\u003c/p\u003e","manuscriptTitle":"Quantum Spectral Analysis of Non-Relativistic Particles in Schwarzschild Spacetime under the Aharonov–Bohm Effect and External Potentials","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-08 18:09:15","doi":"10.21203/rs.3.rs-7103850/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"d9561c92-734c-4e5d-af0d-ea1b9bac8d1d","owner":[],"postedDate":"August 8th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-08-25T07:09:31+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-08 18:09:15","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7103850","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7103850","identity":"rs-7103850","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}