Daniele Pranzetti - On the definition of the spin charge in asymptotically-flat spacetimes 

This talk was part of the Thematic Programme on "Carrollian Physics and Holography" held at the ESI April 2 -- 26, 2024.
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 right asymptotic symmetry algebra to approach this problem is the generalized-BMS algebra gbms, instead of the BMS algebra used hitherto in the literature. We approach the problem of defining the spin charge from the perspective of coadjoint orbits of gbms. We construct the complete set of Casimir invariants that determine gbms coadjoint orbits, using the notion of vorticity for gbms. This allows us to introduce the spin charge for gbms as the generator of its isotropy subalgebra. In order to elucidate the parallelism between our analysis and the Poincar ́e case, we clarify several features of the Poincaré embedding in gbms and introduce the notion of rest frame available only for this extended algebra. This allows us to construct, from the spin generator, the gravitational analog of the Pauli-Lubánski pseudo-vector.

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