Exploring Gravitational Potential and Velocity Profiles through Hypergeometric and Bessel Functions
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".