A trick for passing degenerate points in Ashtekar formulation

Details A trick for passing degenerate points in Ashtekar formulation A trick for passing degenerate points in Ashtekar formulation

1997-04-29

arxiv.org/abs/gr-qc/9704081v1

Phys.Rev. D56 (1997) 2086-2093

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages by RevTeX or 16 pages by LaTeX, 3 eps figures and epsf-style file are included

Scientific paper

10.1103/PhysRevD.56.2086

We examine one of the advantages of Ashtekar's formulation of general relativity: a tractability of degenerate points from the point of view of following the dynamics of classical spacetime. Assuming that all dynamical variables are finite, we conclude that an essential trick for such a continuous evolution is in complexifying variables. In order to restrict the complex region locally, we propose some `reality recovering' conditions on spacetime. Using a degenerate solution derived by pull-back technique, and integrating the dynamical equations numerically, we show that this idea works in an actual dynamical problem. We also discuss some features of these applications.

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