Symmetries of vanishing nonlinear Love numbers of Schwarzschild black holes
Bibliographic record
Abstract
A bstract The tidal Love numbers parametrize the conservative induced tidal response of self-gravitating objects. It is well established that asymptotically-flat black holes in four-dimensional general relativity have vanishing Love numbers. In linear perturbation theory, this result was shown to be a consequence of ladder symmetries acting on black hole perturbations. In this work, we show that a black hole’s tidal response induced by a static, parity-even tidal field vanishes for all multipoles to all orders in perturbation theory. Our strategy is to focus on static and axisymmetric spacetimes for which the dimensional reduction to the fully nonlinear Weyl solution is well-known. We define the nonlinear Love numbers using the point-particle effective field theory, matching with the Weyl solution to show that an infinite subset of the static, parity-even Love number couplings vanish, to all orders in perturbation theory. This conclusion holds even if the tidal field deviates from axisymmetry. Lastly, we discuss the symmetries underlying the vanishing of the nonlinear Love numbers. An $$\mathfrak{s}\mathfrak{l}$$ (2, ℝ) algebra acting on a covariantly-defined potential furnishes ladder symmetries analogous to those in linear theory. This is because the dynamics of the potential are isomorphic to those of a static, massless scalar on a Schwarzschild background. We comment on the connection between the ladder symmetries and the Geroch group that is well-known to arise from dimensional reduction.
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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) | 0.000 | 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 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 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".