Proof of Positivity of Mass for Maximally Sliced, Asymptotically Flat Spacetimes

TL;DR

This paper aims to reformulate the ADM mass in asymptotically flat spacetimes to make its positivity more transparent, addressing a fundamental aspect of mass in General Relativity.

Contribution

The paper presents a new formulation of the ADM mass that clearly demonstrates its positivity for maximally sliced, asymptotically flat spacetimes.

Findings

Reformulated the ADM mass to reveal its positivity

Provided a new perspective on mass positivity in General Relativity

Enhanced understanding of mass properties in specific spacetime slices

Abstract

There exists in General Relativity an unambiguous notion of Mass associated to asymptotically flat spacetimes known as the ADM mass. The standard expression for the same is a surface integral over spatial infinity of a linear combination of spatial deriatives of the three metric adapted to a constant time spatial hypersurface evaluated at infinity. In this form however the positivity of this mass formula is not apparent, so in the following an attempt shall be made to bring this functional into a form where it's positivity is evident.