2004/10/31 by Jörg Frauendiener, Tilman Vogel, Timothy M. Vogel · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Numerical methods for differential equations #Pulsars and Gravitational Waves Research #gr-qc
paper · pdf · doi:10.1088/0264-9381/22/9/019
published as Class.Quant.Grav. 22 (2005) 1769-1793 · 25 pages, 5 figures; v2: small additions, new reference, publication number, classification and keywords added, address fixed; v3: update to match journal version
openalex publication_date 2005/04/12 · arxiv created 2005/08/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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 the context of the Weyl system. This system is the essential hyperbolic part in various formulations of the Einstein equations.