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

Hisa-aki Shinkai and Gen Yoneda
Phys. Rev. D 60, 101502(R) – Published 18 October 1999
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Abstract

We present a set of dynamical equations based on Ashtekar’s extension of the Einstein equation. The system forces the spacetime 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, Hübner, 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.

  • Received 11 May 1999

DOI:https://doi.org/10.1103/PhysRevD.60.101502

©1999 American Physical Society

Authors & Affiliations

Hisa-aki Shinkai*

  • Center for Gravitational Physics and Geometry, 104 Davey Laboratory, Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802-6300

Gen Yoneda

  • Department of Mathematical Sciences, Waseda University, Shinjuku, Tokyo, 169-8555, Japan

  • *Electronic address: shinkai@gravity.phys.psu.edu
  • Electronic address: yoneda@mn.waseda.ac.jp

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Issue

Vol. 60, Iss. 10 — 15 November 1999

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