The existence and stability of the photon spheres and time-like circular orbits in the spacetime of magnetic Gauss–Bonnet black hole
Bibliographic record
Abstract
This paper was devoted to studying the structure of the photon spheres and time-like circular orbits in the magnetic Gauss–Bonnet black hole space–time. Herein, the relationship between the photon spheres, the time-like circular orbits, and the black hole horizons was analyzed. We found that the photon sphere curve of the black hole ends at the horizon curve of the extreme black hole. The outer photon sphere is unstable and the inner photon sphere is stable. However, given that there is physically no inner photon sphere of the black hole inside the event horizon, the black hole has only one unstable photon sphere. Specifically, compact massive objects have at most two photon spheres, i.e., stable and unstable. Moreover, the curve of extremal stable time-like circular orbits ends at the coincidence of the inner and outer photon spheres, whereas the inner time-like circular orbits cannot be inside the photon spheres. Therefore, the extremal stable time-like circular orbits become multivalued, which is related to the existence of the photon sphere. When the photon sphere exists, the extremal stable time-like circular orbits behave as the innermost stable circular orbits. When the photon sphere does not exist, the extremal stable time-like circular orbits have both an innermost stable circular orbit and an outermost stable circular orbit.
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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 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 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".