Improved gauge driver for the generalized harmonic Einstein system
نویسندگان
چکیده
A new gauge driver is introduced for the generalized harmonic (GH) representation of Einstein’s equation. This new driver allows a rather general class of gauge conditions to be implemented in a way that maintains the hyperbolicity of the combined evolution system. This driver is more stable and effective and, unlike previous drivers, allows stable evolutions using the dual-frame evolution technique. Appropriate boundary conditions for this new gauge driver are constructed, and a new boundary condition for the ‘‘gauge’’ components of the spacetime metric in the GH Einstein system is introduced. The stability and effectiveness of this new gauge driver are demonstrated through numerical tests, which impose a new damped-wave gauge condition on the evolutions of single black-hole spacetimes.
منابع مشابه
Generalized harmonic formulation in spherical symmetry
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention in numerical relativity over the past few years, especially as applied to the problem of binary inspiral and merger. A key issue when using the technique is t...
متن کاملTesting outer boundary treatments for the Einstein equations
Various methods of treating outer boundaries in numerical relativity are compared using a simple test problem: a Schwarzschild black hole with an outgoing gravitational wave perturbation. Numerical solutions computed using different boundary treatments are compared to a ‘reference’ numerical solution obtained by placing the outer boundary at a very large radius. For each boundary treatment, the...
متن کاملImplementation of Absorbing Boundary Conditions for the Einstein Equations
Based on a recent study of the linearized Bianchi equations by Buchman and Sarbach, we construct and implement a hierarchy of absorbing boundary conditions for the Einstein equations in generalized harmonic gauge. As a test problem, we demonstrate that we can evolve multipolar gravitational waves without any spurious reflections at linear order in perturbation theory.
متن کاملGlobal existence for the Einstein vacuum equations in wave coordinates
We prove global stability of Minkowski space for the Einstein vacuum equations in harmonic (wave) coordinate gauge for the set of restricted data coinciding with the Schwarzschild solution in the neighborhood of space-like infinity. The result contradicts previous beliefs that wave coordinates are ”unstable in the large” and provides an alternative approach to the stability problem originally s...
متن کاملGauge drivers for the generalized harmonic Einstein equations
Lee Lindblom, Keith D. Matthews, Oliver Rinne, and Mark A. Scheel Theoretical Astrophysics 130-33, California Institute of Technology, Pasadena, California 91125, USA Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom King’s College, Cambridge CB2 1ST, United Kingdom (Received 13 November 2007; publish...
متن کامل