Quadratic Mode Couplings in Rotating Black Holes and Their Detectability
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Bibliographic record
Abstract
Quadratic quasinormal modes encode fundamental properties of black hole spacetimes. They are also one of the key ingredients of nonlinearities of general relativity in the ringdown stage of binary black hole coalescence. In this Letter, we classify all possible quadratic coupling channels of quasinormal modes for a generic Kerr black hole and use a frequency-domain pseudospectral code with hyperboloidal slicing to calculate these couplings. After accounting for all the channels in systems with reflection symmetry, our results become consistent with those extracted from numerical simulations and time-domain fits. This agreement provides a compelling example demonstrating the success of black hole second-order perturbation theory. We also explore potential applications of our calculations in future ringdown data analysis by carrying out a detectability survey for various quadratic modes. We find that a few of them are observationally relevant for third-generation ground-based detectors like Cosmic Explorer, as well as the spaceborne Laser Interferometer Space Antenna.
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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) | 0.001 | 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 | 0.001 |
| 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 it