Bibliographic record
Abstract
Abstract When Gaussian null coordinates are adapted to a Killing horizon, the near-horizon limit is defined by a coordinate rescaling and then by taking the regulator parameter ɛ to be small, as a way of zooming into the horizon hypersurface. In this coordinate setting, it is known that the metric of a non-extremal Killing horizon in the near-horizon limit is divergent, and it has been a common practice to impose extremality in order to set the divergent term to zero. Although the metric is divergent, we show for a class of Killing horizons that the vacuum Einstein’s equations can be separated into a divergent and a finite part, leading to a well-defined minimal set of Einstein’s equations one needs to solve. We extend the result to Einstein gravity minimally coupled to a massless scalar field. We also discuss the case of Einstein gravity coupled to a Maxwell field, in which case the separability holds if the Maxwell potential has non-vanishing components only in the directions of the horizon spatial cross section.
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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) | 0.000 | 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 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".