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Uniqueness and Non-uniqueness in the Einstein Constraints

Harald P. Pfeiffer·James W. York
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Abstract

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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BibTeXRIS

Harald P. Pfeiffer, James W. York. 2005-07-30. Uniqueness and Non-uniqueness in the Einstein Constraints. https://doi.org/10.1103/physrevlett.95.091101

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