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Mass and 3-metrics of non-negative scalar curvature

Robert Bartnik
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Abstract

Physicists believe, with some justification, that there should be a correspondence between familiar properties of Newtonian gravity and properties of solutions of the Einstein equations. The Positive Mass Theorem (PMT), first proved over twenty years ago \cite{SchoenYau79b,Witten81}, is a remarkable testament to this faith. However, fundamental mathematical questions concerning mass in general relativity remain, associated with the definition and properties of quasi-local mass. Central themes are the structure of metrics with non-negative scalar curvature, and the role played by minimal area 2-spheres (black holes).

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Robert Bartnik. 2003-04-18. Mass and 3-metrics of non-negative scalar curvature. https://arxiv.org/abs/math/0304259

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