Orbital mechanics and quasiperiodic oscillation resonances of black holes in Einstein-Æther theory
Bibliographic record
Abstract
In this paper, we study the motion of test particles around two exact charged black hole solutions in Einstein-\AE{}ther theory. Specifically, we first consider the quasiperiodic oscillations (QPOs) and their resonances generated by the particle moving in the Einstein-\AE{}ther black hole and then turn to study the periodic orbits of the massive particles. For QPOs, we drop the usually adopted assumptions ${\ensuremath{\nu}}_{U}={\ensuremath{\nu}}_{\ensuremath{\theta}}$, ${\ensuremath{\nu}}_{L}={\ensuremath{\nu}}_{r}$, and ${\ensuremath{\nu}}_{U}/{\ensuremath{\nu}}_{L}=3/2$ with ${\ensuremath{\nu}}_{U}$ (${\ensuremath{\nu}}_{L}$) and ${\ensuremath{\nu}}_{r}$ (${\ensuremath{\nu}}_{\ensuremath{\theta}}$) being the upper (lower) frequency of QPOs and radial (vertical) epicyclic frequency of the orbiting particles, respectively. Instead, we put-forward a new working ansatz for which the Keplerian radius is much closer to that of the innermost stable circular orbit and explore in detail the effects of the \ae{}ther field on the frequencies of QPOs. We then realize good curves for the frequencies of QPOs, which fit to data of three microquasars very well by ignoring any effects of rotation and magnetic fields. The innermost stable circular orbits (isco) of timelike particles are also analyzed, and we find the isco radius increases with increasing ${c}_{13}$ for the first type black hole while decreases with increasing ${c}_{14}$ for the second one. We also obtain several periodic orbits and find that they share similar taxonomy schemes as the periodic equatorial orbits in the Schwarzschild/Kerr metrics, in addition to exact solutions for certain choices of the Einstein-\AE{} ther parameters. The equations for null geodesics are also briefly considered, where we study circular photon orbits and bending angles for gravitational lensing.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| 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".