BMS symmetries of gravitational scattering

Abstract

After motivating the relevance of the Bondi-Metzner-Sachs (BMS) group over the last decades, we review how concepts such as Penrose diagrams and the covariant phase space formalism can be used to understand the asymptotic structure of asymptotically flat spacetimes (AFS). We then explicitly construct the asymptotic symmetry group of AFS in $3+1$ dimensions, the BMS group. Next, we apply this knowledge to the usual far-field scattering problem in general relativity, which leads to the unravelling of the intrinsic features of gravity in the infrared. In particular, we work out the connections between asymptotic symmetries, soft theorems in quantum field theories and gravitational memory effects. We restrict to the study of this infrared triangle through the lens of supertranslations here, but the analogous features that can be found in the case of superrotations or for other gauge theories are also motivated at the end of our discussion. We conclude with an overview of the implications of the infrared triangle of gravity for the formulation of an approach to quantum gravity through holography, as well as a brief discussion of its potential in tackling the black hole information paradox.

This review article arose from an essay submitted for the partial fulfilment of the requirements for the degree of Master of Advanced Study in Applied Mathematics (Part III of the Mathematical Tripos) at the University of Cambridge, set by Dr. Prahar Mitra and submitted by the author in May 2023. It is aimed at advanced undergraduate students or early postgraduate students willing to learn about the role of asymptotic symmetries in the context of flat space holography, with only basic knowledge of quantum field theory and general relativity assumed.

Note

Another comprehensive review on this topic by Laura Donnay [1] appeared between the submission of this essay and its publication. The present review provides complementary background material and includes explicit derivations, which may be useful to young researchers.