Mixed hyperbolic-second-order-parabolic formulations of general relativity

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7 Scopus citations


Two new formulations of general relativity are introduced. The first one is a parabolization of the Arnowitt-Deser-Misner formulation and is derived by the addition of combinations of the constraints and their derivatives to the right-hand side of the Arnowitt-Deser-Misner evolution equations. The desirable property of this modification is that it turns the surface of constraints into a local attractor because the constraint propagation equations become second-order parabolic independently of the gauge conditions employed. This system may be classified as mixed hyperbolic-second-order parabolic. The second formulation is a parabolization of the Kidder-Scheel-Teukolsky formulation and is a manifestly mixed strongly hyperbolic-second-order-parabolic set of equations, bearing thus resemblance to the compressible Navier-Stokes equations. As a first test, a stability analysis of flat space is carried out and it is shown that the first modification exponentially damps and smoothes all constraint-violating modes. These systems provide a new basis for constructing schemes for long-term and stable numerical integration of the Einstein field equations.

Original languageEnglish (US)
Article number024002
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number2
StatePublished - Jul 3 2008
Externally publishedYes

ASJC Scopus subject areas

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


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