Bibliographic record
Abstract
In the present paper, we consider a rotating black hole moving in a homogeneous massless scalar field. We assume that the field is weak and neglect its backreaction so that the metric at far distance from the black hole is practically flat. In this domain, one can introduce two reference frames, $K$ and $\stackrel{\texttildelow{}}{K}$. The frame $\stackrel{\texttildelow{}}{K}$ is associated with the homogeneous scalar field, in which its constant gradient has only time component. The other frame, $K$, is the frame in which the black hole is at rest. To describe the Kerr metric of the black hole, we use its Kerr-Schild form ${g}_{\ensuremath{\mu}\ensuremath{\nu}}={\ensuremath{\eta}}_{\ensuremath{\mu}\ensuremath{\nu}}+\mathrm{\ensuremath{\Phi}}{l}_{\ensuremath{\mu}}{l}_{\ensuremath{\mu}}$, where ${\ensuremath{\eta}}_{\ensuremath{\mu}\ensuremath{\nu}}$ is the (asymptotic) flat metric in $K$ frame. We find an explicit solution of the scalar field equation, which is regular at the horizon, and properly reproduce the asymptotic form of the scalar field at the infinity. Using this solution, we calculate the fluxes of the energy, momentum and the angular momentum of the scalar field into the black hole. This allows us to derive the equation of motion of the rotating black hole. We discuss main general properties of solutions of these equations and obtain explicit solutions for special type of the motion of the black hole.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".