Algebraic stability analysis of constraint propagation

The divergence of the constraint quantities is a major problem in computational gravity today. Apparently, there are two sources for constraint violations. The use of boundary conditions which are not compatible with the constraint equations inadvertently leads to 'constraint violating modes�...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Frauendiener, Jörg, Vogel, Tilman
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.08.2005
Subjects
Boundary conditions
Boundary value problems
Computation
Divergence
Einstein equations
Formulations
Initial conditions
Mathematical analysis
Propagation modes
Stability analysis
Surface stability
Online AccessGet full text

Cover

More Information
Summary:The divergence of the constraint quantities is a major problem in computational gravity today. Apparently, there are two sources for constraint violations. The use of boundary conditions which are not compatible with the constraint equations inadvertently leads to 'constraint violating modes' propagating into the computational domain from the boundary. The other source for constraint violation is intrinsic. It is already present in the initial value problem, i.e. even when no boundary conditions have to be specified. Its origin is due to the instability of the constraint surface in the phase space of initial conditions for the time evolution equations. In this paper, we present a technique to study in detail how this instability depends on gauge parameters. We demonstrate this for the influence of the choice of the time foliation in context of the Weyl system. This system is the essential hyperbolic part in various formulations of the Einstein equations.
ISSN:2331-8422
DOI:10.48550/arxiv.0410100