Numerical Integration of Nonlinear Wave Equations for General Relativity

Details Numerical Integration of Nonlinear Wave Equations for General Relativity Numerical Integration of Nonlinear Wave Equations for General Relativity

1997-01-10

arxiv.org/abs/gr-qc/9701019v1

Phys.Rev. D55 (1997) 4705-4711

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages (LaTex), 3 figures (ps)

Scientific paper

10.1103/PhysRevD.55.4705

A second-order numerical implementation is given for recently derived nonlinear wave equations for general relativity. The Gowdy T$^3$ cosmology is used as a test bed for studying the accuracy and convergence of simulations of one-dimensional nonlinear waves. The complete freedom in space-time slicing in the present formulation is exploited to compute in the Gowdy line-element. Second-order convergence is found by direct comparison of the results with either analytical solutions for polarized waves, or solutions obtained from Gowdy's reduced wave equations for the more general unpolarized waves. Some directions for extensions are discussed.

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