Limit of quasilocal mass at spatial infinity

TL;DR

This paper investigates the behavior of quasilocal mass at spatial infinity, demonstrating it converges to the ADM mass and explicitly computing limits for specific spacelike surfaces in Schwarzschild spacetime.

Contribution

It establishes the equivalence of quasilocal mass limits with ADM mass and provides explicit calculations for boosted Schwarzschild slices.

Findings

Quasilocal mass limit equals ADM mass at spatial infinity.

Explicit computation for boosted Schwarzschild slices confirms expected energy-momentum.

Results support the consistency of quasilocal mass definitions with classical energy concepts.

Abstract

We study the limit of quasilocal mass defined in [4] and [5] for a family of spacelike 2-surfaces in spacetime. In particular, we show the limit coincides with the ADM mass at spatial infinity. The limit for coordinate spheres of a boosted slice of the Schwarzchild solution is computed explicitly and shown to give the expected energy-momentum four vector.