On the Bartnik extension problem for the static vacuum Einstein equations

Abstract

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.

33 pages, 1 figure. Minor revision of v2. Final version, to appear in Class. Quantum Gravity

References in corpus (1)

• Unique continuation results for Ricci curvature and applications

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