Uniqueness of static vacuum Einstein metrics and the Bartnik quasi-local mass
arXiv:1003.2803
Abstract
We analyse the issue of uniqueness of solutions of the static vacuum Einstein equations with prescribed geometric or Bartnik boundary data. Large classes of examples are constructed where uniqueness fails. We then discuss the implications of this behavior for the Bartnik quasi-local mass. A variational characterization of Bartnik boundary data is also given.
This article is withdrawn, and part of its content has been absorbed into the new version of arXiv:0909.4550