Exploring Gravitational Potential and Velocity Profiles through Hypergeometric and Bessel Functions

Exploring Gravitational Potential and Velocity Profiles through Hypergeometric and Bessel Functions | 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 Exploring Gravitational Potential and Velocity Profiles through Hypergeometric and Bessel Functions Durakhshan Ashraf Qadri, Mir Hameeda, Qudsia Gani, M. C. Rocca This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4143505/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 paper explores the behavior of gravitational potential in the form of Bessel functions and Hypergeo-metric functions[1, 2, 3]. Building upon our earlier research[4, 5] on gravitational potential characterized by Bessel functions[6], we now investigate the gravitational potential as a hypergeometric function. Through various examples and formulations, including Newton’s gravity and Tohline’s gravity[7], we present various forms of gravitational potential and velocity profiles as hypergeometric functions. Additionally, we discuss the combination of the homogeneous hypergeometric solution with the homogeneous Bessel solution, along with Newton’s gravity and Tohline’s gravity. Finally, we present an oscillatory model incorporating both the hypergeometric function and the Bessel function, combined with the Newton potential or the Tohline potential to observe the quantized behavior of speed. To further lend credence to this study and previous work, the authors have proposed a possible interpretation of neutrino oscillations while using the same functional form of gravitational potential as obtained in this paper. Neutrinos have a feeble mass and interact via gravity. These flip their flavour during the course of their flight which is called as neutrino oscillation. So far neutrino oscillation has been described as quantum mechanical phenomenon which arises since the mass eigenstates of neutrinos are not identical with their flavour eigenstates. However, an alternate classical description may be that neutrinos oscillate due to oscillatory nature of gravitational potential. Bessel function Hypergeometric function Quantized speed Oscillatory model Tohline gravity Neutrino oscillation and mass-mixing 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-4143505","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":283099510,"identity":"b184a70c-a53c-4901-ba42-22f157fa03b2","order_by":0,"name":"Durakhshan Ashraf Qadri","email":"","orcid":"","institution":"Government Degree College Tangmarg India","correspondingAuthor":false,"prefix":"","firstName":"Durakhshan","middleName":"Ashraf","lastName":"Qadri","suffix":""},{"id":283099511,"identity":"3cde0cf1-675b-4316-96c3-223861598f17","order_by":1,"name":"Mir Hameeda","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4UlEQVRIiWNgGAWjYBACAyA+8OEHA2MDewOIa0GUFsaDM3uAWngOgLgSRGlhPszDBtQikQDiE6HFXOzwgQM8PDay/TOfX93wo0CCgb+9OwGvFsvZaQkHJCzSjGfczim72QN0mMSZsxvwO+x2jsEBA57DiQ23c9Ju8AC1GEjkEtKS/+FAAtv/xPk3z6Td/EOclhyGAwfYDiRuuMF+7DaRtqQZHGzsSTbeeCaH7baMgQQPEX5Jfvz5zw872XnHjz+7+eaPjRx/ey9+LUiAxwBMEqscBNgfkKJ6FIyCUTAKRhAAAKhGUlR0Ux+wAAAAAElFTkSuQmCC","orcid":"","institution":"Government Degree College Tangmarg India","correspondingAuthor":true,"prefix":"","firstName":"Mir","middleName":"","lastName":"Hameeda","suffix":""},{"id":283099512,"identity":"3beab0b4-e705-49c2-a87b-429ce50a0b73","order_by":2,"name":"Qudsia Gani","email":"","orcid":"","institution":"Government Degree College Pattan","correspondingAuthor":false,"prefix":"","firstName":"Qudsia","middleName":"","lastName":"Gani","suffix":""},{"id":283099513,"identity":"578e5f3d-da71-47dd-b7c1-b92a92212f22","order_by":3,"name":"M. 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