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General-covariant evolution formalism for Numerical Relativity

C. Bona·T. Ledvinka·C. Palenzuela·M. Zacek
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Abstract

A general covariant extension of Einstein\'{}s field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector $Z_μ$. Einstein's solutions are recovered when the additional four-vector vanishes, so that the energy and momentum constraints amount to the covariant algebraic condition $Z_μ=0$. The extended field equations can be supplemented by suitable coordinate conditions in order to provide symmetric hyperbolic evolution systems: this is actually the case for either harmonic coordinates or normal coordinates with harmonic slicing.

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C. Bona, T. Ledvinka, C. Palenzuela, M. Zacek. 2003-02-20. General-covariant evolution formalism for Numerical Relativity. https://doi.org/10.1103/physrevd.67.104005

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