Mass and 3-metrics of non-negative scalar curvature

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).

References in corpus (1)

• A Positive Mass Theorem Based on the Focusing and Retardation of Null Geodesics

Cited by in corpus (6)

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• The Willmore center of mass of initial data sets
• New asymptotically flat static vacuum metrics with near Euclidean boundary data
• On long-time existence for the flow of static metrics with rotational symmetry
• Static solutions from the point of view of comparison geometry