On the Various Extensions of the BMS Group
Romain Ruzziconi
TL;DR
This work analyzes extensions of the BMS symmetry in four dimensions by incorporating superrotations and exploring their phase spaces in first-order gravity formulations. It develops a covariant phase space framework for covariantized Hamiltonian theories, derives generalized BMS and Λ-BMS charge algebras, and establishes a clear flat limit connection between Λ-BMS and generalized BMS. By examining vacuum structure and memory effects, it links superrotations to observable gravitational memory phenomena. It also introduces Λ-BMS boundary conditions via holographic renormalization, showing that the Λ-limit recovers the generalized BMS phase space and charges, thereby enriching the understanding of asymptotic symmetries in spacetimes with (A)dS asymptotics and their flat-space limit.
Abstract
The Bondi-Metzner-Sachs-van der Burg (BMS) group is the asymptotic symmetry group of radiating asymptotically flat spacetimes. It has recently received renewed interest in the context of the flat holography and the infrared structure of gravity. In this thesis, we investigate the consequences of considering extensions of the BMS group in four dimensions with superrotations. In particular, we apply the covariant phase space methods on a class of first order gauge theories that includes the Cartan formulation of general relativity and specify this analysis to gravity in asymptotically flat spacetime. Furthermore, we renormalize the symplectic structure at null infinity to obtain the generalized BMS charge algebra associated with smooth superrotations. We then study the vacuum structure of the gravitational field, which allows us to relate the so-called superboost transformations to the velocity kick/refraction memory effect. Afterward, we propose a new set of boundary conditions in asymptotically locally (A)dS spacetime that leads to a version of the BMS group in the presence of a non-vanishing cosmological constant, called the $Λ$-BMS asymptotic symmetry group. Using the holographic renormalization procedure and a diffeomorphism between Bondi and Fefferman-Graham gauges, we construct the phase space of $Λ$-BMS and show that it reduces to the one of the generalized BMS group in the flat limit.