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General-covariant evolution formalism for Numerical Relativity

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arxiv gr-qc/0302083 v1 pith:R7TOKSE4 submitted 2003-02-20 gr-qc

General-covariant evolution formalism for Numerical Relativity

classification gr-qc
keywords additionalcoordinatescovarianteinsteinequationsevolutionfieldfour-vector
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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Cited by 2 Pith papers

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  2. The Era of Precision in Computational Models of Gravitational Waves

    gr-qc 2026-07 accept novelty 2.0

    Numerical relativity solved the general-relativistic two-body problem in the mid-2000s, supplying the waveform models that enabled LIGO's first gravitational-wave detections.