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Phys. Rev. D 60, 101502(R) (1999) [5 pages]

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

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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

Received 11 May 1999; published 18 October 1999

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.

© 1999 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevD.60.101502
DOI:
10.1103/PhysRevD.60.101502
PACS:
04.20.Ex, 04.20.Fy, 04.20.Ha

*Electronic address: shinkai@gravity.phys.psu.edu

†Electronic address: yoneda@mn.waseda.ac.jp

 
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