Quasilocal mass in general relativity

TL;DR

This paper introduces a new gauge-independent definition of quasilocal mass in general relativity, addressing previous difficulties in choosing background configurations and ensuring nonnegativity and flat spacetime zero value.

Contribution

It proposes a novel, gauge-independent quasilocal mass definition and proves it satisfies key physical properties.

Findings

The new definition is nonnegative for general spacetimes.

It is zero for surfaces in flat spacetime.

The approach resolves background configuration issues.

Abstract

There have been many attempts to define the notion of quasilocal mass for a spacelike 2-surface in spacetime by the Hamilton-Jacobi analysis. The essential difficulty in this approach is to identify the right choice of the background configuration to be subtracted from the physical Hamiltonian. Quasilocal mass should be nonnegative for surfaces in general spacetime and zero for surfaces in flat spacetime. In this letter, we propose a new definition of gauge-independent quasilocal mass and prove that it has the desired properties.