BMS Group at Spatial Infinity: the Hamiltonian (ADM) approach

TL;DR

This paper introduces new boundary conditions at spatial infinity for asymptotically flat spacetimes that are invariant under the BMS group, ensuring well-defined Hamiltonian generators and including key solutions like Schwarzschild and Kerr.

Contribution

It proposes a Hamiltonian, off-shell approach with novel parity conditions that make the BMS group action non trivial at spatial infinity.

Findings

Boundary conditions are invariant under BMS group.

Hamiltonian generators are finite and well-defined.

Includes Schwarzschild and Kerr solutions.

Abstract

New boundary conditions for asymptotically flat spacetimes are given at spatial infinity. These boundary conditions are invariant under the BMS group, which acts non trivially. The boundary conditions fulfill all standard consistency requirements: (i) they make the symplectic form finite; (ii) they contain the Schwarzchild solution, the Kerr solution and their Poincar\'e transforms, (iii) they make the Hamiltonian generators of the asymptotic symmetries integrable and well-defined (finite). The boundary conditions differ from the ones given earlier in the literature in the choice of the parity conditions. It is this different choice of parity conditions that makes the action of the BMS group non trivial. Our approach is purely Hamiltonian and off-shell throughout.