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Numerical Relativity: Evolving Spacetime

Author

Listed:
  • 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)

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.

Suggested Citation

  • C. Bona & J. Massó, 1993. "Numerical Relativity: Evolving Spacetime," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 4(04), pages 883-907.
    • Handle: RePEc:wsi:ijmpcx:v:04:y:1993:i:04:n:s0129183193000690
    DOI: 10.1142/S0129183193000690
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