Einstein constraints: Uniqueness and nonuniqueness in the conformal thin sandwich approach
Abstract
We study the appearance of multiple solutions to certain decompositions of Einstein's constraint equations. Pfeiffer and York recently reported the existence of two branches of solutions for a particular family of background data in the extended conformal thin-sandwich decomposition. We show that the Hamiltonian constraint alone, when expressed in a certain way, admits two branches of solutions with properties very similar to those found by Pfeiffer and York. We construct these two branches analytically for a constant-density star in spherical symmetry, but argue that this behavior is more general. In the case of the Hamiltonian constraint this nonuniqueness is well known to be related to the sign of one particular term, and we argue that the extended conformal thin-sandwich equations contain a similar term that causes the breakdown of uniqueness.
Additional Information
©2007 The American Physical Society (Received 24 October 2006; published 7 February 2007) We would like to thank Edward Malec and Darragh Walsh for helpful comments, as well as the Isaac Newton Institute and the California Institute of Technology for hospitality during various stages of this work. This research was supported in part by a grant from the Sherman Fairchild Foundation, by NSF grant No. PHY-0601459 and by NASA grant No. NNG05GG52G to Caltech, as well as by NSF Grant No. PHY-0456917 to Bowdoin College.Files
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Additional details
- Eprint ID
- 7400
- Resolver ID
- CaltechAUTHORS:BAUprd07
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2007-02-09Created from EPrint's datestamp field
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2021-11-08Created from EPrint's last_modified field