Another proof of the positive energy theorem in gravity

TL;DR

This paper presents a simplified proof of the positive energy theorem in gravity by employing a new coordinate system and leveraging asymptotic symmetries, making the positivity of gravitational energy more transparent.

Contribution

It introduces a novel coordinate choice and gauge condition that clarify the positivity of gravitational energy using asymptotic symmetries in four-dimensional spacetimes.

Findings

Energy expression simplifies in the new coordinates.

Positivity of energy becomes more transparent.

Proof relies on asymptotic symmetries, especially supertranslations.

Abstract

We show that gravitational energy expression simplifies when a new set of coordinates that satisfies a certain asymptotic gauge condition is used. Compared to the ADM formula, positivity of the energy is more transparent in this new construction. Our proof relies on the asymptotic symmetries (specifically supertranslations) of the asymptotically flat spacetimes at spatial infinity in four dimensions.