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arXiv · 0909.4550

On the Bartnik extension problem for the static vacuum Einstein equations

Michael T. Anderson·Marcus A. Khuri
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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.

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Michael T. Anderson, Marcus A. Khuri. 2013-05-04. On the Bartnik extension problem for the static vacuum Einstein equations. https://doi.org/10.1088/0264-9381%2F30%2F12%2F125005

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