Uniqueness and Non-uniqueness in the Einstein Constraints

Details Uniqueness and Non-uniqueness in the Einstein Constraints Uniqueness and Non-uniqueness in the Einstein Constraints

2005-04-29

arxiv.org/abs/gr-qc/0504142v2

Phys.Rev.Lett. 95 (2005) 091101

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages, 4 figures; abstract and introduction rewritten

Scientific paper

10.1103/PhysRevLett.95.091101

The conformal thin sandwich (CTS) equations are a set of four of the Einstein equations, which generalize the Laplace-Poisson equation of Newton's theory. We examine numerically solutions of the CTS equations describing perturbed Minkowski space, and find only one solution. However, we find {\em two} distinct solutions, one even containing a black hole, when the lapse is determined by a fifth elliptic equation through specification of the mean curvature. While the relationship of the two systems and their solutions is a fundamental property of general relativity, this fairly simple example of an elliptic system with non-unique solutions is also of broader interest.

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