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Title: Generalized harmonic spatial coordinates and hyperbolic shift conditions

Abstract

We propose a generalization of the condition for harmonic spatial coordinates analogous to the generalization of the harmonic time slices introduced by Bona et al., and closely related to dynamic shift conditions recently proposed by Lindblom and Scheel, and Bona and Palenzuela. These generalized harmonic spatial coordinates imply a condition for the shift vector that has the form of an evolution equation for the shift components. We find that in order to decouple the slicing condition from the evolution equation for the shift it is necessary to use a rescaled shift vector. The initial form of the generalized harmonic shift condition is not spatially covariant, but we propose a simple way to make it fully covariant so that it can be used in coordinate systems other than Cartesian. We also analyze the effect of the shift condition proposed here on the hyperbolicity of the evolution equations of general relativity in 1+1 dimensions and 3+1 spherical symmetry, and study the possible development of blowups. Finally, we perform a series of numerical experiments to illustrate the behavior of this shift condition.

Authors:
; ; ;  [1];  [2];  [1];  [3]
  1. Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A.P. 70-543, Mexico D.F. 04510 (Mexico)
  2. Theoretical Physics Institute, University of Jena, Max-Wien-Platz 1, 07743, Jena (Germany)
  3. (Germany)
Publication Date:
OSTI Identifier:
20774539
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevD.72.124018; (c) 2005 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; COORDINATES; COSMOLOGY; EQUATIONS; GENERAL RELATIVITY THEORY; SPACE-TIME; SYMMETRY; VECTORS

Citation Formats

Alcubierre, Miguel, Corichi, Alejandro, Nunez, Dario, Salgado, Marcelo, Gonzalez, Jose A., Reimann, Bernd, and Max Planck Institut fuer Gravitationsphysik, Albert Einstein Institut, Am Muehlenberg 1, 14476 Golm. Generalized harmonic spatial coordinates and hyperbolic shift conditions. United States: N. p., 2005. Web. doi:10.1103/PhysRevD.72.124018.
Alcubierre, Miguel, Corichi, Alejandro, Nunez, Dario, Salgado, Marcelo, Gonzalez, Jose A., Reimann, Bernd, & Max Planck Institut fuer Gravitationsphysik, Albert Einstein Institut, Am Muehlenberg 1, 14476 Golm. Generalized harmonic spatial coordinates and hyperbolic shift conditions. United States. doi:10.1103/PhysRevD.72.124018.
Alcubierre, Miguel, Corichi, Alejandro, Nunez, Dario, Salgado, Marcelo, Gonzalez, Jose A., Reimann, Bernd, and Max Planck Institut fuer Gravitationsphysik, Albert Einstein Institut, Am Muehlenberg 1, 14476 Golm. Thu . "Generalized harmonic spatial coordinates and hyperbolic shift conditions". United States. doi:10.1103/PhysRevD.72.124018.
@article{osti_20774539,
title = {Generalized harmonic spatial coordinates and hyperbolic shift conditions},
author = {Alcubierre, Miguel and Corichi, Alejandro and Nunez, Dario and Salgado, Marcelo and Gonzalez, Jose A. and Reimann, Bernd and Max Planck Institut fuer Gravitationsphysik, Albert Einstein Institut, Am Muehlenberg 1, 14476 Golm},
abstractNote = {We propose a generalization of the condition for harmonic spatial coordinates analogous to the generalization of the harmonic time slices introduced by Bona et al., and closely related to dynamic shift conditions recently proposed by Lindblom and Scheel, and Bona and Palenzuela. These generalized harmonic spatial coordinates imply a condition for the shift vector that has the form of an evolution equation for the shift components. We find that in order to decouple the slicing condition from the evolution equation for the shift it is necessary to use a rescaled shift vector. The initial form of the generalized harmonic shift condition is not spatially covariant, but we propose a simple way to make it fully covariant so that it can be used in coordinate systems other than Cartesian. We also analyze the effect of the shift condition proposed here on the hyperbolicity of the evolution equations of general relativity in 1+1 dimensions and 3+1 spherical symmetry, and study the possible development of blowups. Finally, we perform a series of numerical experiments to illustrate the behavior of this shift condition.},
doi = {10.1103/PhysRevD.72.124018},
journal = {Physical Review. D, Particles Fields},
number = 12,
volume = 72,
place = {United States},
year = {Thu Dec 15 00:00:00 EST 2005},
month = {Thu Dec 15 00:00:00 EST 2005}
}