Mixed Hyperbolic - Second-Order Parabolic Formulations of General Relativity

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dc.creatorPaschalidis, Vasileios
dc.date2007-04-22
dc.date2008-03-18
dc.date.accessioned2026-07-07T11:41:02Z
dc.date.available2026-07-07T11:41:02Z
dc.descriptionTwo new formulations of general relativity are introduced. The first one is a parabolization of the Arnowitt, Deser, Misner (ADM) formulation and is derived by addition of combinations of the constraints and their derivatives to the right-hand-side of the ADM 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.
dc.description19 pages, two column, references added, two proofs of well-posedness added, content changed to agree with submitted version to PRD
dc.identifierhttps://arxiv.org/abs/0704.2861
dc.identifierhttp://arxiv.org/abs/0704.2861
dc.identifierPhys.Rev.D78:024002,2008
dc.identifierdoi:10.1103/PhysRevD.78.024002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/200397
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleMixed Hyperbolic - Second-Order Parabolic Formulations of General Relativity
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