Symmetric hyperbolic system in the Ashtekar formulation

Abstract

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, Leguizamón 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.

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

References in corpus (5)

• First order hyperbolic formalism for Numerical Relativity
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• Treating instabilities in a hyperbolic formulation of Einstein's equations
• Einstein's equations in Ashtekar's variables constitute a symmetric hyperbolic system
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