Near-horizon BMS symmetries as fluid symmetries

Abstract

The Bondi-van der Burg-Metzner-Sachs (BMS) group is the asymptotic symmetry group of asymptotically flat gravity. Recently, Donnay et al. have derived an analogous symmetry group acting on black hole event horizons. For a certain choice of boundary conditions, it is a semidirect product of $\mathrm{Diff}(S^2)$, the smooth diffeomorphisms of the two-sphere, acting on $C^{\infty }(S^2)$, the smooth functions on the two-sphere. We observe that the same group appears in fluid dynamics as symmetries of the compressible Euler equations. We relate these two realizations of $\mathrm{Diff}(S^2)⋉C^{\infty }(S^2)$ using the black hole membrane paradigm. We show that the Lie-Poisson brackets of membrane paradigm fluid charges reproduce the near-horizon BMS algebra. The perspective presented here may be useful for understanding the BMS algebra at null infinity.

18 pages, 3 figures

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