Generalized harmonic spatial coordinates and hyperbolic shift conditions

Alcubierre, Miguel; Corichi, Alejandro; Gonzalez, Jose A.; Nunez, Dario; Reimann, Bernd; Salgado, Marcelo

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Generalized harmonic spatial coordinates and hyperbolic shift conditions

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Reimann, Bernd
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Alcubierre, M., Corichi, A., Gonzalez, J. A., Nunez, D., Reimann, B., & Salgado, M. (2005). Generalized harmonic spatial coordinates and hyperbolic shift conditions. Physical Review D, 72(12): 124018.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-4F3A-2

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. 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. 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.