Bibliographic record
Abstract
The excitation of quadratic quasinormal modes is an important nonlinear phenomenon for a Kerr black hole ringing at a specific linear mode. The amplitude of this second-order effect is proportional to the square of the linear mode amplitude, with the ratio being linked to the nature of the Kerr black hole. Focusing on the linear $(l=m=2,n=0)$ mode, we compute the dependency of the ratio on the dimensionless spin of the black hole, ranging up to 0.99, with the method applicable for more general mode couplings. Our calculation makes use of the frequency-domain, second-order Teukolsky equation, which involves two essential steps: (a) analytically reconstructing the metric through the Chrzanowski-Cohen-Kegeles approach and (b) numerically solving the second-order Teukolsky equation using the shooting method along a complex contour. We find that the spin dependence of the ratio shows a strong correlation with the angular overlap between parent and child modes, providing qualitative insights into the origin of the dependence. Depending on the nature of the angular overlap, the ratio decreases with spin in scenarios such as the channel $(l=m=2,n=0)\ifmmode\times\else\texttimes\fi{}(l=m=2,n=0)\ensuremath{\rightarrow}(l=m=4)$ or increases in situations like $(l=m=2,n=0)\ifmmode\times\else\texttimes\fi{}(l=m=2,n=0)\ensuremath{\rightarrow}(l=5,m=4)$. For both cases, the ratios do not vanish in the extremal limit. Our studies may offer insights into the search for quadratic quasinormal modes from numerical relativity and gravitational wave detections. As a byproduct, we find that the Weyl scalars can be concisely expressed with the Hertz potential.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".