Algebraic stability analysis of constraint propagation

• Published in: arXiv.org
• Main Authors: Frauendiener, Jörg, Vogel, Tilman
• Format: Paper
• Language: English
• 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
• DOI: 10.48550/arxiv.0410100

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.