| Constructing hyperbolic systems in the Ashtekar formulation of general relativity (2008) | |||||||||||||
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| Hyperbolic formulation of equations of motion is an essential technique for proving well-posedness of the Cauchy problem of a system, and is also helpful for stable long time evolution in numerical applications. We present three kinds of hyperbolic systems in the Ashtekar formulation of general relativity for Lorentzian vacuum spacetime. We show several (I) weakly hyperbolic, (II) diagonalizable hyperbolic and (III) symmetric hyperbolic systems, with discussions of required gauge conditions and reality conditions. In order to construct a first-order symmetric hyperbolic system, we add terms from the constraint equations to the evolution equations with appropriate combinations, which is the same technique used by Iriondo, Leguizam'on and Reula. However our system is different from theirs in the points that we primarily use Hermiticity of a characteristic matrix of the system to define our system symmetric, and in the way of treating reality conditions. 1 Introduction Hyperbolic formul... | |||||||||||||
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