Black Hole Information and Thermodynamics pp 91-94 | Cite as

# Asymptotic Symmetries in General Relativity and Black Hole Hair

## Abstract

We consider asymptotic symmetries, which characterize the infrared (IR) structure of general relativity. In a general relativistic space-time, these asymptotic symmetries were first considered in the 1960’s by Bondi, van der Burg, Metzner, and Sachs (Proc R Soc Lond A Math Phys Eng Sci, 269:21–52, 1962, [17], Proc R Soc Lond A Math Phys Eng Sci, 270:103–126, 1962, [18]). Informed by the notion that flat space-times are generally invariant under the Poincaré group, they expected to find this as the asymptotic symmetry group of asymptotically flat space-times as well. However, the asymptotic symmetry group will turn out to be an infinite-dimensional extension of the Poincaré group. These asymptotic symmetries, knwon as BMS-transformations, are special kinds of diffeomorphisms which can be subdivided into *supertranslations* and *superrotations*. Asymptotic symmetries are also present in gauge theories such as QED and QCD, where they are related to so-called *large gauge transformations*, namely those that do not go to zero at infinity (He et al. JHEP 10:112, 2014, [19]). An important point is that these asymptotic symmetries act as global symmetries despite the fact that they are constructed from gauge symmetries i.e. even though they act non-trivially on the Hilbert space of the system.