Static spheres around spherically symmetric black hole spacetime
Bibliographic record
Abstract
Unique features of particle orbits produce novel signatures of gravitational observable phenomena and are quite useful in testing compact astrophysical objects in general relativity or modified theories of gravity. Here we observe a representative example that a static, spherically symmetric black hole solution with nonlinear electrodynamics admits static points at finite radial distance. Each static point thus produces a static sphere, on which a massive test particle can remain at rest at arbitrary latitudes with respect to an asymptotic static observer. As a result, the well-known static Dyson spheres can be implemented by such orbits. More interestingly, employing a topological argument, we disclose that stable and unstable static spheres (if they exist) always come in pairs in an asymptotically flat spacetime. In contrast to this, the counterpart naked singularity has one more stable static sphere than the unstable one. Our results have potential applications in testing black holes in standard Maxwell and nonlinear electrodynamics, as well as in uncovering the underlying astronomical observation effects in other gravitational theories beyond general relativity.
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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 | 0.000 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".