${\mathrm{BMS}}_3$ invariant fluid dynamics at null infinity

Abstract

We revisit the boundary dynamics of asymptotically flat, three dimensional gravity. The boundary is governed by a momentum conservation equation and an energy conservation equation, which we interpret as fluid equations, following the membrane paradigm. We reformulate the boundary's equations of motion as Hamiltonian flow on the dual of an infinite-dimensional, semi-direct product Lie algebra equipped with a Lie-Poisson bracket. This gives the analogue for boundary fluid dynamics of the Marsden-Ratiu-Weinstein formulation of the compressible Euler equations on a manifold, $M$, as Hamiltonian flow on the dual of the Lie algebra of $\mathrm{Diff}(M)⋉C^{\infty }(M)$. The Lie group for boundary fluid dynamics turns out to be $\mathrm{Diff}(S^1){⋉}_{\mathrm{Ad}}\mathfrak{vir}$, with central charge $c=3/G$. This gives a new derivation of the centrally extended, three-dimensional Bondi-van der Burg-Metzner-Sachs (${\mathrm{BMS}}_3$) group. The relationship with fluid dynamics helps to streamline and physically motivate the derivation. For example, the central charge, $c=3/G$, is simply read off of a fluid equation in much the same way as one reads off a viscosity coefficient. The perspective presented here may useful for understanding the still mysterious four-dimensional BMS group.

15 pages

References in corpus (11)

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• Evidence for a New Soft Graviton Theorem
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• The quantum mechanics of perfect fluids
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• Near-horizon BMS symmetries as fluid symmetries
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Cited by in corpus (19)

• Carrollian Perspective on Celestial Holography
• Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids
• Conformal Carroll Scalars with Boosts
• Brown-York charges at null boundaries
• Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite $\sqrt{T\bar{T}}$ deformations
• Gauges in Three-Dimensional Gravity and Holographic Fluids
• Near-horizon BMS symmetries as fluid symmetries
• Symmetries of the Black Hole Interior and Singularity Regularization
• Integrable systems with BMS${}_3$ Poisson structure and the dynamics of locally flat spacetimes
• Hydro & Thermo Dynamics at Causal Boundaries, Examples in 3d Gravity
• Thomas Precession for Dressed Particles
• BMS${}_3$ Mechanics and the Black Hole Interior
• Quantum Area Fluctuations from Gravitational Phase Space
• Asymptotic symmetries of three dimensional gravity and the membrane paradigm
• Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs
• Fefferman-Graham and Bondi Gauges in the Fluid/Gravity Correspondence
• Relativistic Fluids, Hydrodynamic Frames and their Galilean versus Carrollian Avatars
• $\mathrm{SDiff}(S^2)$ and the orbit method
• On deformations and extensions of $\text{Diff}(S^2)$