Abstract
The Bondi-van der Burg-Metzner-Sachs (BMS) group is the asymptotic symmetry group of asymptotically flat spacetime. It is infinite dimensional and entails an infinite number of conservation laws. According to the black hole membrane paradigm, null infinity (in asymptotically flat spacetime) and black hole event horizons behave like fluid membranes. The fluid dynamics of the membrane is governed by an infinite set of symmetries and conservation laws. Our main result is to point out that the infinite set of symmetries and conserved charges of the BMS group and the membrane paradigm are the same. This relationship has several consequences. First, it sheds light on the physical interpretation of BMS conservation laws. Second, it generalizes the BMS conservation laws to arbitrary subregions of arbitrary null surfaces. Third, it clarifies the identification of the superrotation subgroup of the BMS group. We briefly comment on the black hole information problem.
Highlights
This new perspective has a number of advantages
According to the black hole membrane paradigm, null infinity and black hole event horizons behave like fluid membranes
It clarifies the physical interpretation of BMS conservation laws
Summary
The membrane paradigm attaches a 2+1 dimensional fluid stress-energy tensor to null surfaces. We review the definition of the membrane stress-energy tensor. The stress-energy tensor is an integral over the extrinsic curvature of the membrane, so we first define extrinsic curvature. The cutoff surface is “stretched infinity,” a large but finite sphere. For tensors on 3+1 dimensional spacetime, lower case roman indices a, b, . For tensors on the 2+1 dimensional membrane, and upper case roman indices A, B, . For tensors on constant-time slices of the membrane. Where the upper sign applies at event horizons and the lower sign applies at null infinity. Where upper signs apply at future event horizons and past null infinity, while lower signs apply at past event horizons and future null infinity.
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