Trick for passing degenerate points in the Ashtekar formulation

Gen Yoneda, Hisa-aki Shinkai, Akika Nakamichi
1997 Physical Review D, Particles and fields  
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
more » ... 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.
doi:10.1103/physrevd.56.2086 fatcat:teszo42nrrezngxg77imoygfe4