On the Bartnik extension problem for the static vacuum Einstein equations
Differential Geometry
2015-05-14 v3 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.0909.4550,
title = {On the Bartnik extension problem for the static vacuum Einstein equations},
author = {Michael T. Anderson and Marcus A. Khuri},
journal= {arXiv preprint arXiv:0909.4550},
year = {2015}
}
Comments
33 pages, 1 figure. Minor revision of v2. Final version, to appear in Class. Quantum Gravity