Systematic study of event horizons and pathologies of parametrically deformed Kerr spacetimes
Bibliographic record
Abstract
In general relativity, all black holes in vacuum are described by the Kerr metric, which has only two independent parameters: the mass and the spin. The unique dependence on these two parameters is known as the ``no-hair'' theorem. This theorem may be tested observationally by using electromagnetic or gravitational-wave observations to map the spacetime around a candidate black hole and measure potential deviations from the Kerr metric. Several parametric frameworks have been constructed for tests of the no-hair theorem. Due to the uniqueness of the Kerr metric, any such parametric framework must violate at least one of the assumptions of the no-hair theorem. This can lead to pathologies in the spacetime, such as closed timelike curves or singularities, which may hamper using the metric in the strong-field regime. In this paper, I analyze in detail several parametric frameworks and show explicitly the manner in which they differ from the Kerr metric. I calculate the coordinate locations of event horizons in these metrics, if any exist, using methods adapted from the numerical relativity literature. I identify the regions where each parametric deviation is unphysical as well as the range of coordinates and parameters for which each spacetime remains a regular extension of the Kerr metric and is, therefore, suitable for observational tests of the no-hair theorem.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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".