On the Numerical Integration of Einstein's Field Equations

Details On the Numerical Integration of Einstein's Field Equations On the Numerical Integration of Einstein's Field Equations

1998-10-20

arxiv.org/abs/gr-qc/9810065v1

Phys.Rev. D59 (1999) 024007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, 3 figures, RevTeX, to appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.59.024007

Many numerical codes now under development to solve Einstein's equations of general relativity in 3+1 dimensional spacetimes employ the standard ADM form of the field equations. This form involves evolution equations for the raw spatial metric and extrinsic curvature tensors. Following Shibata and Nakamura, we modify these equations by factoring out the conformal factor and introducing three ``connection functions''. The evolution equations can then be reduced to wave equations for the conformal metric components, which are coupled to evolution equations for the connection functions. We evolve small amplitude gravitational waves and make a direct comparison of the numerical performance of the modified equations with the standard ADM equations. We find that the modified form exhibits much improved stability.

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