Numerical evolution of black holes with a hyperbolic formulation of general relativity

Mark A. Scheel, Thomas W. Baumgarte, Gregory B. Cook, Stuart L. Shapiro, Saul A. Teukolsky

Research output: Contribution to journalArticlepeer-review


We describe a numerical code that solves Einstein’s equations for a Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation introduced by Choquet-Bruhat and York. This is the first time this formulation has been used to evolve a numerical spacetime containing a black hole. We excise the hole from the computational grid in order to avoid the central singularity. We describe in detail a causal differencing method that should allow one to stably evolve a hyperbolic system of equations in three spatial dimensions with an arbitrary shift vector, to second-order accuracy in both space and time. We demonstrate the success of this method in the spherically symmetric case.

Original languageEnglish (US)
Pages (from-to)6320-6335
Number of pages16
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number10
StatePublished - 1997

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)

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