Bibliographic record
Abstract
We discuss static spherically symmetric metrics which represent nonsingular black holes in four- and higher-dimensional spacetime. We impose a set of restrictions, such as a regularity of the metric at the center $r=0$ and Schwarzschild asymptotic behavior at large $r$. We assume that the metric besides mass $M$ contains an additional parameter $\ensuremath{\ell}$, which determines the scale where modification of the solution of the Einstein equations becomes significant. We require that the modified metric obeys the limiting curvature condition; that is, its curvature is uniformly restricted by the value $\ensuremath{\sim}{\ensuremath{\ell}}^{\ensuremath{-}2}$. We also make a ``more technical'' assumption that the metric coefficients are rational functions of $r$. In particular, the invariant $(\ensuremath{\nabla}r{)}^{2}$ has the form ${P}_{n}(r)/{\stackrel{\texttildelow{}}{P}}_{n}(r)$, where ${P}_{n}$ and ${\stackrel{\texttildelow{}}{P}}_{n}$ are polynomials of the order of $n$. We discuss first the case of four dimensions. We show that when $n\ensuremath{\le}2$ such a metric cannot describe a nonsingular black hole. For $n=3$ we find a suitable metric, which besides $M$ and $\ensuremath{\ell}$ contains a dimensionless numerical parameter. When this parameter vanishes, the obtained metric coincides with Hayward's one. The characteristic property of such spacetimes is $\ensuremath{-}{\ensuremath{\xi}}^{2}=(\ensuremath{\nabla}r{)}^{2}$, where ${\ensuremath{\xi}}^{2}$ is a timelike at infinity Killing vector. We describe a possible generalization of a nonsingular black-hole metric to the case when this equality is violated. We also obtain a metric for a charged nonsingular black hole obeying similar restrictions as the neutral one and construct higher dimensional models of neutral and charged black holes.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.003 | 0.005 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.010 | 0.001 |
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".