On the Definition of the Spin Charge in Asymptotically-Flat Spacetimes
Bibliographic record
Abstract
We propose a solution to a classic problem in gravitational physics consisting of defining the spin associated with asymptotically-flat spacetimes. We advocate that the correct asymptotic symmetry algebra to approach this problem is the generalized-BMS algebra $\textsf{gbms}$ instead of the BMS algebra used hitherto in the literature for which a notion of spin is generically unavailable. We approach the problem of defining the spin charges from the perspective of coadjoint orbits of $\textsf{gbms}$ and construct the complete set of Casimir invariants that determine $\textsf{gbms}$ coadjoint orbits, using the notion of vorticity for $\textsf{gbms}$. This allows us to introduce spin charges for $\textsf{gbms}$ as the generators of area-preserving diffeomorphisms forming its isotropy subalgebra. To elucidate the parallelism between our analysis and the Poincaré case, we clarify several features of the Poincaré embedding in $\textsf{gbms}$ and reveal the presence of condensate fields associated with the symmetry breaking from $\textsf{gbms}$ to Poincaré. We also introduce the notion of a rest frame available only for this extended algebra. This allows us to construct, from the spin generator, the gravitational analog of the Pauli--Lubański pseudo-vector. Finally, we obtain the $\textsf{gbms}$ moment map, which we use to construct the gravitational spin charges and gravitational Casimirs from their dual algebra counterparts.
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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 | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".