Positivity of Quasilocal Mass

TL;DR

This paper introduces new definitions for quasilocal energy and momentum of spacelike 2-surfaces, demonstrating positivity under certain conditions and extending Brown and York's work on quasilocal energy.

Contribution

It proposes novel definitions of quasilocal energy and momentum with positivity properties, advancing the understanding of energy in general relativity.

Findings

Quasilocal energy is positive unless spacetime is flat.

Definitions are consistent with Brown and York's framework.

Positivity holds under local energy conditions.

Abstract

Motivated by the important work of Brown adn York on quasilocal energy, we propose definitions of quasilocal energy and momentum surface energy of a spacelike 2-surface with positive intrinsic curvature in a spacetime. We show that the quasilocal energy of the boundary of a compact spacelike hypersurface which satisfies the local energy condition is strictly positive unless the spacetime is flat along the spacelike hypersurface.