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

Beyer, Horst; Sarbach, Olivier

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

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Beyer, Horst
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Beyer, H., & Sarbach, O. (2004). On the well posedness of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's field equations. Physial Review D, 70: 104004.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-518C-0

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-Masso 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.