Bibliographic record
Abstract
The radial differential equations associated with separable perturbations of Kerr-Newman black holes are known to admit Liouvillian (closed-form) solutions for constrained frequencies and black hole parameters. In this paper, we show that the parameter constraints are satisfied exactly in the case of no rotation and thereby obtain a countable infinity of exact purely damped quasi-normal modes of fields on a Reissner-Nordstrom background at special values of the black hole charge-mass ratio. We show that with rotation the parameter constraints for Liouvillian quasi-normal modes are satisfied approximately in two distinct physical scenarios, where analytical approximations for angular eigenvalues are known. We arrive at functional expressions for quasi-normal frequencies and wave-functions in the case of near-extremal slow rotation and in a particular case of highly damped scalar modes of Kerr and Kerr-Newman. In the near-extremal case, our formulas extend a recent result of Hod to electromagnetic and gravitational perturbations.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".