Tidally induced multipole moments of a nonrotating black hole vanish to all post-Newtonian orders
Bibliographic record
Abstract
The tidal Love numbers of a black hole vanish, and this is often taken to imply that the hole's tidally induced multipole moments vanish also. An obstacle to establishing a link between these statements is that the multipole moments of individual bodies are not defined in general relativity, when the bodies are subjected to a mutual gravitational interaction. In a previous publication [Phys. Rev. D 103, 064023 (2021)] I promoted the view that individual multipole moments can be defined when the mutual interaction is sufficiently weak to be described by a post-Newtonian expansion. In this view, a compact body is perceived far away as a skeletonized post-Newtonian object with a multipole structure, and the multipole moments can then be related to the body's Love numbers. I expand on this view, and demonstrate that all static, tidally induced, mass multipole moments of a nonrotating black hole vanish to all post-Newtonian orders. The proof rests on a perturbative solution to the Einstein-Maxwell equations that describes an electrically charged particle placed in the presence of a charged black hole. The gravitational attraction between particle and black hole is balanced by electrostatic repulsion, and the system is in an equilibrium state. The particle provides a tidal environment to the black hole, and the multipole moments vanish for this environment. I argue that the vanishing is robust, and applies to all slowly-varying tidal environments. The black hole's charge can be as small as desired (though not identically zero); by continuity, the multipole moments of an electrically neutral black hole will continue to vanish.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".