Pfeiffer, Harald P. and York, James W., Jr. (2005) Uniqueness and nonuniqueness in the Einstein constraints. Physical Review Letters, 95 (9). Art. No. 091101. ISSN 0031-9007 http://resolver.caltech.edu/CaltechAUTHORS:PFEprl05
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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 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 nonunique solutions is also of broader interest.
|Additional Information:||©2005 The American Physical Society. Received 28 April 2005; published 26 August 2005. The authors thank Lee Lindblom, Lawrence Kidder, and Mark Scheel for helpful discussions; the numerical code has been developed in collaboration with Lawrence Kidder and Mark Scheel. This work was supported in part by NSF Grant Nos. PHY-0244906 and PHY-0099568 to Caltech and Grant Nos. PHY-0407762, PHY-0311817, and PHY-0216986 to Cornell. H. P. gratefully acknowledges support from the Sherman Fairchild Foundation.|
|Subject Keywords:||Einstein field equations; black holes; space-time configurations|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||20 Mar 2006|
|Last Modified:||26 Dec 2012 08:48|
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