Symmetric hyperbolic system in the Ashtekar formulation

Details Symmetric hyperbolic system in the Ashtekar formulation Symmetric hyperbolic system in the Ashtekar formulation

1998-03-24

arxiv.org/abs/gr-qc/9803077v2

Phys.Rev.Lett. 82 (1999) 263-266

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages, RevTeX, to appear in Phys. Rev. Lett., Comments added, refs updated

Scientific paper

10.1103/PhysRevLett.82.263

We present a first-order symmetric hyperbolic system in the Ashtekar formulation of general relativity for vacuum spacetime. We add terms from constraint equations to the evolution equations with appropriate combinations, which is the same technique used by Iriondo, Leguizam\'on and Reula [Phys. Rev. Lett. 79, 4732 (1997)]. However our system is different from theirs in the points that we primarily use Hermiticity of a characteristic matrix of the system to characterize our system "symmetric", discuss the consistency of this system with reality condition, and show the characteristic speeds of the system.

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