A stress tensor for asymptotically flat spacetime

TL;DR

This paper introduces a method to compute the boundary stress tensor in asymptotically flat spacetimes, successfully reproducing known charges and extending to BMS symmetries, with implications for understanding gravitational energy and momentum.

Contribution

It proposes a new procedure for calculating the boundary stress tensor in asymptotically flat spacetimes, aligning with known charges and exploring BMS symmetries.

Findings

Successfully reproduces Kerr black hole charges

Computes BMS symmetry charges using the new stress tensor

Interprets the stress tensor as an expectation value

Abstract

In this article, we propose a procedure for calculating the boundary stress tensor of a gravitational theory in asymptotic flat spacetime. As a case study, the stress tensor correctly reproduces the Brown-York charges for the Kerr blackhole i.e. mass and angular momentum. In asymptotic flat spacetime, there are asymptotic symmetries called BMS symmetries. We also compute the charges associated with these symmetries with the proposed stress tensor. The asymptotic charges can be compared with the Wald-Zoupas method. Our result for the stress tensor can be interpreted as the expectation value for the boundary stress tensor.