Initial boundary value problems for Einstein's field equations and geometric uniqueness

Details Initial boundary value problems for Einstein's field equations and geometric uniqueness Initial boundary value problems for Einstein's field equations and geometric uniqueness

2009-03-30

arxiv.org/abs/0903.5160v1

Gen.Rel.Grav.41:1947-1966,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages

Scientific paper

10.1007/s10714-009-0800-3

While there exist now formulations of initial boundary value problems for Einstein's field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two different approaches we discuss how this difficulty arises under general assumptions. So far it is not known whether it can be overcome without imposing conditions on the geometry of the boundary. We point out a natural and important class of initial boundary value problems which may offer possibilities to arrive at a fully covariant formulation.

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