New solutions of initial conditions in general relativity

We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a simple form. In general the mean curvature H is non-constant...

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Bibliographic Details
Published inClassical and quantum gravity Vol. 31; no. 11; pp. 115001 - 115019
Main Authors Tafel, J, Jó wikowski, M
Format Journal Article
LanguageEnglish
Published IOP Publishing 07.06.2014
Subjects
conformal method
Curvature
Exact solutions
Exteriors
Initial conditions
initial constraints
Invariants
marginally trapped surface
Mathematical analysis
Quantum gravity
Symmetry
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Summary:We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a simple form. In general the mean curvature H is non-constant and g is not conformally flat. In the generic case with the symmetry we obtain general solution in an explicit form. In other cases solutions are given up to quadrature. We also find a class of explicit solutions without symmetries which generalizes data induced by the Kerr metric or other metrics related to the Ernst equation. The conformal method of Lichnerowicz, Choquet-Bruhat and York is used to prove solvability of the Hamiltonian constraint if H vanishes. Existence of marginally outer trapped surfaces in initial manifold is discussed.
Bibliography:CQG-100323
ObjectType-Article-1
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ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/31/11/115001