Asymptotic Structure and Bondi-Metzner-Sachs group in General Relativity

TL;DR

This paper explores the asymptotic structure of space-time in general relativity, focusing on the properties of the BMS group, its mathematical foundations, and its relation to the Poincaré group, with implications for modern theoretical physics.

Contribution

It provides a comprehensive analysis of the BMS group, including its generators, structure, and relation to Poincaré symmetry, advancing understanding of asymptotic symmetries in general relativity.

Findings

Derived the generators of the BMS group.

Analyzed the group structure and Lie algebra of BMS.

Discussed the relation between BMS and Poincaré groups.

Abstract

In this work the asymptotic structure of space-time and the main properties of the Bondi-Metzner-Sachs (BMS) group, which is the asymptotic symmetry group of asymptotically flat space-times, are analysed. Every chapter, except the fourth, begins with a brief summary of the topics that will be dealt through it and an introduction to the main concepts. The work can be divided into three principal parts. The first part includes the first two chapters and is devoted to the development of the mathematical tools that will be used throughout all of the work. In particular we will introduce the notion of space-time and will review the main features of what is referred to as its causal structure and the spinor formalism, which is fundamental in the understanding of the asymptotic properties. In the second part, which includes the third, fourth and fifth chapters, the topological and geometrical properties of null infinity, I, and the behaviour of the fields in its neighbourhood will be studied. Particular attention will be paid to the peeling property. The last part is completely dedicated to the BMS group. We will solve the asymptotic Killing equations and find the generators of the group, discuss its group structure and Lie algebra and eventually try to obtain the Poincar\'e group as its normal subgroup. The work ends with a brief conclusion in which are reviewed the main modern applications of the BMS group.