The static extension problem in General Relativity

Details The static extension problem in General Relativity The static extension problem in General Relativity

2009-09-24

arxiv.org/abs/0909.4550v2

Mathematics

Differential Geometry

33 pages; significant revision of v.1

Scientific paper

We develop a framework for understanding the existence of asymptotically flat solutions to the static vacuum Einstein equations with prescribed boundary data consisting of the induced metric and mean curvature on a 2-sphere. A partial existence result is obtained, giving a partial resolution of a conjecture of Bartnik on such static vacuum extensions. The existence and uniqueness of such extensions is closely related to Bartnik's definition of quasi-local mass.

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