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Uniqueness and Non-uniqueness in the Einstein Constraints | | Harald P. Pfeiffer
; James W. York
; | | Date: |
29 Apr 2005 | | Journal: | Phys.Rev.Lett. 95 (2005) 091101 | | Subject: | gr-qc | | Affiliation: | Caltech) and James W. York (Cornell | | 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. | | Source: | arXiv, gr-qc/0504142 | | Services: | Forum | Review | PDF | Favorites | |
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