On the Definition of the Spin Charge in Asymptotically-Flat Spacetimes

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 $\text{gbms}$ 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 $\text{gbms}$ and construct the complete set of Casimir invariants that determine $\text{gbms}$ coadjoint orbits, using the notion of vorticity for $\text{gbms}$. This allows us to introduce spin charges for $\text{gbms}$ 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 $\text{gbms}$ and reveal the presence of condensate fields associated with the symmetry breaking from $\text{gbms}$ 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 $\text{gbms}$ moment map, which we use to construct the gravitational spin charges and gravitational Casimirs from their dual algebra counterparts.

72 Pages + Appendices + References = 119 Pages

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Cited by in corpus (2)

• Asymptotic Higher Spin Symmetries II: Noether Realization in Gravity
• Asymptotic Higher Spin Symmetries IV: Einstein-Yang-Mills Theory