Evolving Einstein's field equations with matter: The "hydro without hydro" test

Thomas W. Baumgarte, Scott A. Hughes, Stuart L. Shapiro

Research output: Contribution to journalArticlepeer-review


We include matter sources in Einstein's field equations and show that our recently proposed 3+1 evolution scheme can stably evolve strong-field solutions. We insert in our code known matter solutions, namely the Oppenheimer-Volkoff solution for a static star and the Oppenheimer-Snyder solution for homogeneous dust sphere collapse to a black hole, and evolve the gravitational field equations. We find that we can evolve stably static, strong-field stars for arbitrarily long times and can follow dust sphere collapse accurately well past black hole formation. These tests are useful diagnostics for fully self-consistent, stable hydrodynamical simulations in 3+1 general relativity. Moreover, they suggest a successive approximation scheme for determining gravitational waveforms from strong-field sources dominated by longitudinal fields, such as binary neutron stars: approximate quasi-equilibrium models can serve as sources for the transverse field equations, which can be evolved without having to re-solve the hydrodynamical equations ("hydro without hydro").

Original languageEnglish (US)
Article number087501
Pages (from-to)1-4
Number of pages4
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number8
StatePublished - Oct 15 1999

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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