Symmetric hyperbolicity and consistent boundary conditions for second-order Einstein equations

Details Symmetric hyperbolicity and consistent boundary conditions for second-order Einstein equations Symmetric hyperbolicity and consistent boundary conditions for second-order Einstein equations

2004-03-03

arxiv.org/abs/gr-qc/0403019v1

Phys.Rev. D70 (2004) 044032

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, 1 figure, revtex4

Scientific paper

10.1103/PhysRevD.70.044032

We present two families of first-order in time and second-order in space formulations of the Einstein equations (variants of the Arnowitt-Deser-Misner formulation) that admit a complete set of characteristic variables and a conserved energy that can be expressed in terms of the characteristic variables. The associated constraint system is also symmetric hyperbolic in this sense, and all characteristic speeds are physical. We propose a family of constraint-preserving boundary conditions that is applicable if the boundary is smooth with tangential shift. We conjecture that the resulting initial-boundary value problem is well-posed.

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