Relativistic quantum effects in compact astrophysical objects: a harmonic oscillator approach

Relativistic quantum effects in compact astrophysical objects: a harmonic oscillator approach | 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 Relativistic quantum effects in compact astrophysical objects: a harmonic oscillator approach Olakunle Ogunjobi, Jude D. Koffa This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4752308/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 In this study, we examine relativistic quantum harmonic oscillators and their applications to compact astrophysical objects. Using a refined Hermite polynomial series approach, we derive analytical solutions for energy eigenvalues and normalized eigenfunctions to order $v^2/c^2$, extending beyond previous approximations. A computational model, validated against these analytical results, explores neutron star and black hole parameters. Several percent of the total energies of these compact objects are affected by relativistic corrections. Our model predicts relativistic corrections of up to 20% for oscillation frequencies in highly magnetized neutron stars and modifications of 1-5% to innermost stable circular orbits around stellar-mass black holes. As compared to non-relativistic equations of state, we observe measurable deviations in mass-radius relations in neutron stars. These modifications have implications for accretion disk dynamics and associated emissions, potentially detectable with next-generation X-ray timing observations. Relativistic quantum mechanics Neutron stars Black holes Astrophysical oscillations 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. 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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-4752308","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":337728533,"identity":"6318e5c4-741a-4371-adcb-8cff971f05ed","order_by":0,"name":"Olakunle Ogunjobi","email":"data:image/png;base64,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","orcid":"","institution":"University of Calgary","correspondingAuthor":true,"prefix":"","firstName":"Olakunle","middleName":"","lastName":"Ogunjobi","suffix":""},{"id":337728534,"identity":"796fb6d4-6cb2-4054-a5a9-d47a3bd38fd6","order_by":1,"name":"Jude D. 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