Abstract
The coadjoint representation of the BMS group in four dimensions is constructed in a formulation that covers both the sphere and the punctured plane. The structure constants are worked out for different choices of bases. The conserved current algebra of non-radiative asymptotically flat spacetimes is explicitly interpreted in these terms.
Highlights
The BMS group [1,2,3,4,5] is the symmetry group of four-dimensional asymptotically flat spacetimes at null infinity
The coadjoint representation of the BMS group in four dimensions is constructed in a formulation that covers both the sphere and the punctured plane
Whereas unitary irreducible representations of the BMS group are directly relevant for the quantum theory [8,9,10], the coadjoint representation is intimately connected to classical solution space through the momentum map
Summary
The BMS group [1,2,3,4,5] is the symmetry group of four-dimensional asymptotically flat spacetimes at null infinity. In the case of the sphere, we explicitly identify the coadjoint representation in the gravitational data of non-radiative spacetimes. Note that our conventions for these derivatives differ somewhat from those originally introduced in [16,17,18] for related reasons The description applies both to the “global” and “local” versions of the algebra [19,20,21,22], which are studied explicitly in sections 5 and 6, respectively. Central extensions are the familiar ones directly related to the Virasoro group and algebra Neither of these simplifications occur in four dimensions. Central extensions that are relevant in the gravitational context are of a different nature [27], and will not be considered here
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