First order hyperbolic formalism for numerical relativity

C. Bona, J. Massó, E. Seidel, J. Stela

Research output: Contribution to journalArticlepeer-review


The causal structure of Einstein's evolution equations is considered. We show that in general they can be written as a first-order system of balance laws for any choice of slicing or shift. We also show how certain terms in the evolution equations, which can lead to numerical inaccuracies, can be eliminated by using the Hamiltonian constraint. Furthermore, we show that the entire system is hyperbolic when the time coordinate is chosen in an invariant algebraic way, and for any fixed choice of the shift. This is achieved by using the momentum constraints in such a way that no additional space or time derivatives of the equations need to be computed. The slicings that allow hyperbolicity in this formulation belong to a large class, including harmonic, maximal, and many others that have been commonly used in numerical relativity. We provide details of some of the advanced numerical methods that this formulation of the equations allows, and we also discuss certain advantages that a hyperbolic formulation provides when treating boundary conditions.

Original languageEnglish (US)
Pages (from-to)3405-3415
Number of pages11
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number6
StatePublished - 1997
Externally publishedYes

ASJC Scopus subject areas

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


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