Numerical integration of Einstein's field equations

Thomas W. Baumgarte, Stuart L. Shapiro

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1-7
Number of pages7
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number2
StatePublished - Jan 15 1999

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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