# Near-horizon BMS symmetries as fluid symmetries

## TL;DR

This paper reveals that the near-horizon BMS symmetries of black holes are mathematically equivalent to fluid symmetries in the compressible Euler equations, connecting gravitational and fluid dynamics through the membrane paradigm.

## Contribution

It demonstrates the equivalence of near-horizon BMS symmetries and fluid symmetries, providing a new perspective on black hole horizon symmetries via fluid dynamics.

## Key findings

- The near-horizon BMS algebra matches the Lie-Poisson brackets of membrane paradigm fluid charges.
- The same symmetry group appears in both black hole horizons and fluid dynamics.
- This connection may help understand BMS algebra at null infinity.

## 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 ${\rm Diff}(S^2)$, 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 ${\rm Diff}(S^2)\ltimes C^\infty(S^2)$ 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.