Spherical collapse in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>gravity and the Belinskii-Khalatnikov-Lifshitz conjecture
Bibliographic record
Abstract
Spherical scalar collapse in $f(R)$ gravity is studied numerically in double-null coordinates in Einstein frame. Dynamics in the vicinity of the singularity of the formed black hole is examined via mesh refinement and asymptotic analysis. Before the collapse, the scalar degree of freedom ${f}^{\ensuremath{'}}$ is coupled to a physical scalar field, and general relativity is restored. During the collapse, the major energy of the physical scalar field moves to the center. As a result, ${f}^{\ensuremath{'}}$ loses the coupling and becomes light, and gravity transits from general relativity to $f(R)$ gravity. Due to strong gravity from the singularity and the low mass of ${f}^{\ensuremath{'}}$, ${f}^{\ensuremath{'}}$ will cross the minimum of the potential and approach zero. Therefore, the dynamical solution is significantly different from the static solution of the black hole in $f(R)$ gravity---it is not the de Sitter-Schwarzschild solution as one might have expected. ${f}^{\ensuremath{'}}$ tries to suppress the evolution of the physical scalar field, which is a dark energy effect. As the singularity is approached, metric terms are dominant over other terms. The Kasner solution for spherical scalar collapse in $f(R)$ theory is obtained and confirmed by numerical results. These results support the Belinskii-Khalatnikov-Lifshitz conjecture well.
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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 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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".