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

## TL;DR

This paper reviews the asymptotic structure of gravity at spatial infinity in four dimensions, focusing on boundary conditions, asymptotic symmetries, and the BMS group, with detailed analysis of charges and algebra.

## Contribution

It introduces twisted parity boundary conditions that ensure finiteness and integrability, clarifying the structure of asymptotic symmetries and charges in four-dimensional gravity.

## Key findings

- Asymptotic symmetry group is the infinite-dimensional BMS group.
- Boundary conditions lead to well-defined charges and algebra.
- The presentation is pedagogical and self-contained.

## 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.