General-covariant evolution formalism for Numerical Relativity

Details General-covariant evolution formalism for Numerical Relativity General-covariant evolution formalism for Numerical Relativity

2003-02-20

arxiv.org/abs/gr-qc/0302083v1

Phys.Rev.D67:104005,2003

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

10.1103/PhysRevD.67.104005

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 $Z_\mu$. Einstein's solutions are recovered when the additional four-vector vanishes, so that the energy and momentum constraints amount to the covariant algebraic condition $Z_\mu=0$. 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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