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On the Proof of the Positive Mass Conjecture
in General Relativity
Richard Schoen and Shing-Tung Yau

Abstract. Let M be a space-time whose local mass density is non-negative
everywhere. Then we prove that the total mass of M as viewed from spatial
infinity (the ADM mass) must be positive unless M is the flat Minkowski
space-time. (So far we are making the reasonable assumption of the existence of
a maximal spacelike hypersurface. We will treat this topic separately.) We can
generalize our result to admit wormholes in the initial-data set. In fact, we
show that the total mass associated with each asymptotic regime is nonnegative
with equality only if the space-time is flat.

0. Introduction
This is the second part of our paper on scalar curvature of a three-dimensional
manifold and its relation to general relativity. The problem in general relativity
that we address is the following: An isolated gravitating system having nonnegative
local mass density must have non-negative total mass, measured
gravitationally at spatial infinity.