Asymptotic structure of the gravitational field in five spacetime dimensions: Hamiltonian analysis

TL;DR

This paper analyzes the asymptotic structure of gravity in five-dimensional spacetime using Hamiltonian methods, revealing a complex algebra of symmetries including angle-dependent supertranslations.

Contribution

It develops a Hamiltonian framework for higher-dimensional gravity, characterizes the BMS$_5$ symmetry algebra, and constructs a linearized Poincaré subalgebra within it.

Findings

BMS$_5$ contains a four-fold family of supertranslations

The non-linear algebra of asymptotic symmetries is characterized

A linear presentation of the Poincaré subalgebra is constructed

Abstract

We develop the analysis of the asymptotic properties of gravity in higher spacetime dimensions $D$, with a particular emphasis on the case $D=5$. Our approach deals with spatial infinity and is Hamiltonian throughout. It is shown that the asymptotic symmetry algebra BMS$_5$, which is realized non linearly, contains a four-fold family of angle-dependent supertranslations. The structure of this non-linear algebra is investigated and a presentation in which the Poincar\'e subalgebra is linearly realized is constructed. Invariance of the energy is studied. Concluding comments on higher dimensions $D \geq 6$ are also given.