Tidally induced multipole moments of a charged material body
Bibliographic record
Abstract
We define and calculate the mass multipole moments of a material body of mass $M$ and electric charge $Q$ tidally deformed by a particle of mass $m\ensuremath{\ll}M$ and charge $q\ensuremath{\ll}Q$ placed at a distance ${r}_{0}$ from the body. Given $Q/M$ and ${r}_{0}$, we choose $q/m$ so that the gravitational attraction between body and particle is balanced by the electrostatic repulsion; the system can then be maintained in a static state. The multipole moments are defined in a setting in which the body's self-gravity is allowed to be strong, but the mutual gravity between body and companion is required to be weak. In this setting, the body is described in full general relativity, in terms of a perturbed metric and electromagnetic potential characterized by tidal constants, and the mutual gravity is described within the post-Newtonian approximation to general relativity, in terms of objects with a multipole structure. Matching the different descriptions of the same field delivers a relation between the tidal constants and the multipole moments. In our implementation of this program, the calculation is performed in full Einstein-Maxwell theory (as a linearized perturbation of the unperturbed field), without appeal to a post-Newtonian approximation. After the fact we take $M/{r}_{0}$ to be small and carry out an expansion of the metric in powers of $M/r$ to obtain the multipole moments and associated Love numbers. The calculations are performed for a body made up of a perfect fluid with a uniform ratio of charge to mass densities, governed by a polytropic equation of state. We show that the Love numbers of a charged body in a situation of balanced gravitational and electrostatic forces are negative. The statement remains true even when $Q/M$ is very small, and we conclude that the tidal deformability of a charged body is radically different from that of an uncharged object, for which the Love numbers are positive.
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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 | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".