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.