NUMERICAL RELATIVITY: EVOLVING SPACETIME

C. Bona and J. Massó
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C. Bona: Departament de Física, Universitat de les Illes Balears, E-07071 Palma de Mallorca, Spain
J. Massó: Departament de Física, Universitat de les Illes Balears, E-07071 Palma de Mallorca, Spain

International Journal of Modern Physics C (IJMPC), 1993, vol. 04, issue 04, 883-907

Abstract: The construction of numerical solutions of Einstein's General Relativity equations is formulated as an initial-value problem. The space-plus-time(3 + 1)decomposition of the spacetime metric tensor is used to discuss the structure of the field equations. The resulting evolution system is shown to depend in a crucial way on the coordinate gauge. The mandatory use of singularity avoiding coordinate conditions (like maximal slicing or similar gauges) is explained. A brief historical review of Numerical Relativity is included, showing the enormous effort in constructing codes based in these gauges, which lead to non-hyperbolic evolution systems, using "ad hoc" numerical techniques. A new family of first order hyperbolic evolution systems for the vacuum Einstein field equations in the harmonic slicing gauge is presented. This family depends on a symmetric3 × 3array of parameters which can be used to scale the dynamical variables in future numerical applications.

Keywords: 04.20.Cv (search for similar items in EconPapers)
Date: 1993
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DOI: 10.1142/S0129183193000690

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