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 journalArticle


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 [Formula Presented] where [Formula Presented] 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 [Formula Presented] We discuss the implications for three-dimensional simulations.

Original languageEnglish (US)
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number4
StatePublished - Jan 1 1998

ASJC Scopus subject areas

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

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