Coulombic contribution to angular momentum flux in general relativity
Bibliographic record
Abstract
The flux of angular momentum in electromagnetism cannot be expressed entirely in terms of the field's radiative degrees of freedom. Its expression also involves Coulombic pieces of the field, in the form of a charge aspect $q(\ensuremath{\theta},\ensuremath{\phi})$, a function of polar angles whose integral gives the total charge of the system. Guided by the strong analogy between radiative processes in electromagnetism and gravitation, we ask whether the flux of angular momentum in general relativity might also involve Coulombic pieces of the gravitational field. Further, we ask whether such terms might have been missed in the past by specializing the flux to sources of gravitational waves that are at rest with respect to the frame in which the flux is evaluated. To answer these questions, we bring together the Landau-Lifshitz formulation of the Einstein field equations, which provides specific definitions for angular momentum and its associated flux, and the Bondi formalism, which provides a systematic expansion of the metric of an asymptotically flat spacetime in inverse powers of the distance away from the matter distribution. We obtain a new expression for the flux of angular momentum, which is not restricted to sources of gravitational waves at rest nor to periodic sources. We show that our new expression is equivalent to the standard formula used in the literature when these restrictions are put in place. We find that, contrary to expectations based on the analogy between electromagnetism and gravitation, the flux of angular momentum in general relativity can be expressed entirely in terms of the field's radiative degrees of freedom. In contrast to electromagnetism, no Coulombic information is required to calculate the flux of angular momentum in general relativity.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".