Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-04-22
Phys.Rev.D78:024002,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
19 pages, two column, references added, two proofs of well-posedness added, content changed to agree with submitted version to
Scientific paper
10.1103/PhysRevD.78.024002
Two 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.
No associations
LandOfFree
Mixed Hyperbolic - Second-Order Parabolic Formulations of General Relativity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Mixed Hyperbolic - Second-Order Parabolic Formulations of General Relativity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mixed Hyperbolic - Second-Order Parabolic Formulations of General Relativity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-194350