Treating instabilities in a hyperbolic formulation of Einstein's equations

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

Research output: Contribution to journalArticlepeer-review


We have recently constructed a numerical code that evolves a spherically symmetric spacetime using a hyperbolic formulation of Einstein's equations. For the case of a Schwarzschild black hole, this code works well at early times, but quickly becomes inaccurate on a time scale of (10-100)M, where M is the mass of the hole. We present an analytic method that facilitates the detection of instabilities. Using this method, we identify a term in the evolution equations that leads to a rapidly growing mode in the solution. After eliminating this term from the evolution equations by means of algebraic constraints, we can achieve free evolution for times exceeding 10 000M. We discuss the implications for three-dimensional simulations.

Original languageEnglish (US)
Article number044020
Pages (from-to)440201-4402012
Number of pages3961812
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number4
StatePublished - Aug 15 1998

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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