On the structure and applications of the Bondi-Metzner-Sachs group

TL;DR

This paper provides a comprehensive pedagogical review of the Bondi-Metzner-Sachs group, exploring its derivation, properties, and significance in asymptotically flat space-times, with applications to gravitational scattering and quantum gravity.

Contribution

It offers a modern, geometrical derivation of the BMS group and discusses its algebra, subgroups, and relevance to black hole physics and quantum gravity.

Findings

Derivation of the BMS group using classical and conformal methods

Analysis of the BMS algebra and its subgroups including Poincaré

Review of BMS invariance in gravitational scattering phenomena

Abstract

This work is a pedagogical review dedicated to a modern description of the Bondi-Metzner-Sachs group. The curved space-times that will be taken into account are the ones that suitably approach, at infinity, Minkowski space-time. In particular we will focus on asymptotically flat space-times. In this work the concept of asymptotic symmetry group of those space-times will be studied. In the first two sections we derive the asymptotic group following the classical approach which was basically developed by Bondi, van den Burg, Metzner and Sachs. This is essentially the group of transformations between coordinate systems of a certain type in asymptotically flat space-times. In the third section the conformal method and the notion of asymptotic simplicity are introduced, following mainly the works of Penrose. This section prepares us for another derivation of the Bondi-Metzner-Sachs group which will involve the conformal structure, and is thus more geometrical and fundamental. In the subsequent sections we discuss the properties of the Bondi-Metzner-Sachs group, e.g. its algebra and the possibility to obtain as its subgroup the Poincar\'e group, as we may expect. The paper ends with a review of the Bondi-Metzner-Sachs invariance properties of classical gravitational scattering discovered by Strominger, that are finding application to black hole physics and quantum gravity in the literature.