Nonrotating black hole in a post-Newtonian tidal environment. II.
Bibliographic record
Abstract
In the first part of the paper we construct the metric of a tidally deformed, nonrotating black hole. The metric is presented as an expansion in powers of $r/b\ensuremath{\ll}1$, in which $r$ is the distance to the black hole and $b$ the characteristic length scale of the tidal field---the typical distance to the remote bodies responsible for the tidal environment. The metric is expanded through order $(r/b{)}^{4}$ and written in terms of a number of tidal multipole moments, the gravitoelectric moments ${\mathcal{E}}_{ab}$, ${\mathcal{E}}_{abc}$, ${\mathcal{E}}_{abcd}$, and the gravitomagnetic moments ${\mathcal{B}}_{ab}$, ${\mathcal{B}}_{abc}$, ${\mathcal{B}}_{abcd}$. It differs from the similar construction of Poisson and Vlasov in that the tidal perturbation is presented in Regge-Wheeler gauge instead of the light-cone gauge employed previously. In the second part of the paper we determine the tidal moments by matching the black-hole metric to a post-Newtonian metric that describes a system of bodies with weak mutual gravity. This extends the previous work of Taylor and Poisson (Paper I in this sequence), which computed only the leading-order tidal moments, ${\mathcal{E}}_{ab}$ and ${\mathcal{B}}_{ab}$. The matching is greatly facilitated by the Regge-Wheeler form of the black-hole metric, and this motivates the work carried out in the first part of the paper. The tidal moments are calculated accurately through the first post-Newtonian approximation, and at this order they are independent of the precise nature of the compact body. The moments therefore apply equally well to a rotating black hole, or to a (rotating or nonrotating) neutron star. As an application of this formalism, we examine the intrinsic geometry of a tidally deformed event horizon and describe it in terms of a deformation function that represents a quadrupolar and octupolar tidal bulge.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".