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Einstein constraints: Uniqueness and nonuniqueness in the conformal thin sandwich approach

Baumgarte, Thomas W. and Murchadha, Niall Ó and Pfeiffer, Harald P. (2007) Einstein constraints: Uniqueness and nonuniqueness in the conformal thin sandwich approach. Physical Review D, 75 (4). Art. No. 044009. ISSN 2470-0010. doi:10.1103/PhysRevD.75.044009. https://resolver.caltech.edu/CaltechAUTHORS:BAUprd07

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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.


Item Type:Article
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https://doi.org/10.1103/PhysRevD.75.044009DOIUNSPECIFIED
ORCID:
AuthorORCID
Pfeiffer, Harald P.0000-0001-9288-519X
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.
Issue or Number:4
DOI:10.1103/PhysRevD.75.044009
Record Number:CaltechAUTHORS:BAUprd07
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:BAUprd07
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7400
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:09 Feb 2007
Last Modified:08 Nov 2021 20:42

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