Well-posedness of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's field equations

2004/06/01 by Horst R. Beyer, Horst Beyer, Olivier Sarbach · 7 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Pulsars and Gravitational Waves Research #gr-qc

paper · pdf · doi:10.1103/physrevd.70.104004

published as Phys.Rev.D70:104004,2004

arxiv created 2004/06/01 · openalex publication_date 2004/11/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a well posed initial value formulation of the Baumgarte-Shapiro-Shibata-Nakamura form of Einstein's equations with gauge conditions given by a Bona-Mass'o--like slicing condition for the lapse and a frozen shift. This is achieved by introducing extra variables and recasting the evolution equations into a first order symmetric hyperbolic system. We also consider the presence of artificial boundaries and derive a set of boundary conditions that guarantee that the resulting initial-boundary value problem is well posed, though not necessarily compatible with the constraints. In the case of dynamical gauge conditions for the lapse and shift we obtain a class of evolution equations which are strongly hyperbolic and so yield well posed initial value formulations.

Citations

• The Cauchy problem for quasi-linear symmetric hyperbolic systems

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