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

TL;DR

The paper analyzes gravity in four-dimensional spacetimes at spatial infinity within the Hamiltonian framework, showing that twisted parity boundary conditions render the action finite and the Lorentz boosts integrable while preserving a nontrivial BMS4 symmetry. It derives explicit surface terms and charges for translations, supertranslations, angular momentum, and boosts, and demonstrates that the asymptotic symmetry algebra at spatial infinity reproduces the BMS4 structure known from null infinity. The authors present two equivalent approaches to achieve boost integrability—imposing a gauge choice that sets certain radial-angular components to zero, or adding a boundary term to the symplectic structure—both yielding the same physical charges. The work unifies the spatial and null infinity pictures and provides a pedagogical, self-contained derivation with clear implications for foundational questions in gravitational infrared structure and future quantum considerations.

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.