Uniqueness of static vacuum Einstein metrics and the Bartnik quasi-local mass

Marcus A. Khuri, Michael T. Anderson

Publication date: 14 March 2010

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.

Mathematics Subject Classification ID

Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05)

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