Numerical integration of Einstein’s field equations

Thomas W. Baumgarte and Stuart L. Shapiro
Phys. Rev. D 59, 024007 – Published 7 December 1998
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Abstract

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.

  • Received 1 July 1998

DOI:https://doi.org/10.1103/PhysRevD.59.024007

©1998 American Physical Society

Authors & Affiliations

Thomas W. Baumgarte

  • Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

Stuart L. Shapiro

  • Departments of Physics and Astronomy and NCSA, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

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Vol. 59, Iss. 2 — 15 January 1999

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