Asymptotically constrained and real-valued system based on Ashtekar's variables

Abstract

We present a set of dynamical equations based on Ashtekar's extension of the Einstein equation. The system forces the space-time to evolve to the manifold that satisfies the constraint equations or the reality conditions or both as the attractor against perturbative errors. This is an application of the idea by Brodbeck, Frittelli, Huebner and Reula who constructed an asymptotically stable (i.e., constrained) system for the Einstein equation, adding dissipative forces in the extended space. The obtained systems may be useful for future numerical studies using Ashtekar's variables.

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References in corpus (4)

• Einstein's Equations with Asymptotically Stable Constraint Propagation
• Symmetric hyperbolic system in the Ashtekar formulation
• Einstein's equations in Ashtekar's variables constitute a symmetric hyperbolic system
• A trick for passing degenerate points in Ashtekar formulation

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• Hyperbolic formulations and numerical relativity II: Asymptotically constrained systems of the Einstein equations
• Numerical Relativity and Inhomogeneous Cosmologies
• Adjusted ADM systems and their expected stability properties: constraint propagation analysis in Schwarzschild spacetime
• Weyl Curvature Evolution System for GR