The asymptotic structure of gravity at spatial infinity in four spacetime dimensions

Abstract

A review of our results on the asymptotic structure of gravity at spatial infinity in four spacetime dimensions is given. Finiteness of the action and integrability of the asymptotic Lorentz boost generators are key criteria that we implement through appropriate boundary conditions. These conditions are `twisted parity conditions', expressing that the leading order of the asymptotic fields obey strict parity conditions under the sphere antipodal map up to an improper gauge transformation. The asymptotic symmetries are shown to form the infinite-dimensional BMS group, which has a non trivial action. The charges and their algebra are worked out. The presentation aims at being self-contained and at possessing a pedagogical component.

31 pages, review article dedicated to Andrei Slavnov on the occasion of his 80th birthday, appendix C added in version 2

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• BMS Group at Spatial Infinity: the Hamiltonian (ADM) approach
• Soft Hair as a Soft Wig
• Asymptotic symmetries of electromagnetism at spatial infinity
• Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial infinity
• Gravitational dressing, soft charges, and perturbative gravitational splitting
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Cited by in corpus (5)

• Dual gravitational charges and soft theorems
• The (super)conformal BMS${}_3$ algebra
• BMS algebra from residual gauge invariance in light-cone gravity
• BMS algebra as an extension of the Poincaré symmetry in light-cone gravity
• Asymptotic charges for spin-1 and spin-2 fields at the critical sets of null infinity