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Title: 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.

Authors:
 [1];  [2];  [3]
  1. Department of Physics and Astronomy, Bowdoin College, Brunswick, Maine 04011 (United States)
  2. Physics Department, University College, Cork (Ireland)
  3. Theoretical Astrophysics, California Institute of Technology, Pasadena, California 91125 (United States)
Publication Date:
OSTI Identifier:
21011074
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.75.044009; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COSMOLOGICAL MODELS; COSMOLOGY; HAMILTONIANS; MATHEMATICAL SOLUTIONS; SPHERICAL CONFIGURATION; SYMMETRY

Citation Formats

Baumgarte, Thomas W., Murchadha, Niall O, and Pfeiffer, Harald P.. Einstein constraints: Uniqueness and nonuniqueness in the conformal thin sandwich approach. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.044009.
Baumgarte, Thomas W., Murchadha, Niall O, & Pfeiffer, Harald P.. Einstein constraints: Uniqueness and nonuniqueness in the conformal thin sandwich approach. United States. doi:10.1103/PHYSREVD.75.044009.
Baumgarte, Thomas W., Murchadha, Niall O, and Pfeiffer, Harald P.. Thu . "Einstein constraints: Uniqueness and nonuniqueness in the conformal thin sandwich approach". United States. doi:10.1103/PHYSREVD.75.044009.
@article{osti_21011074,
title = {Einstein constraints: Uniqueness and nonuniqueness in the conformal thin sandwich approach},
author = {Baumgarte, Thomas W. and Murchadha, Niall O and Pfeiffer, Harald P.},
abstractNote = {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.},
doi = {10.1103/PHYSREVD.75.044009},
journal = {Physical Review. D, Particles Fields},
number = 4,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}