Symmetric hyperbolic system in the Ashtekar formulation
General Relativity and Quantum Cosmology
2009-10-31 v2 Mathematical Physics
math.MP
Abstract
We present a first-order symmetric hyperbolic system in the Ashtekar formulation of general relativity for vacuum spacetime. We add terms from constraint equations to the evolution equations with appropriate combinations, which is the same technique used by Iriondo, Leguizam\'on and Reula [Phys. Rev. Lett. 79, 4732 (1997)]. However our system is different from theirs in the points that we primarily use Hermiticity of a characteristic matrix of the system to characterize our system "symmetric", discuss the consistency of this system with reality condition, and show the characteristic speeds of the system.
Cite
@article{arxiv.gr-qc/9803077,
title = {Symmetric hyperbolic system in the Ashtekar formulation},
author = {Gen Yoneda and Hisa-aki Shinkai},
journal= {arXiv preprint arXiv:gr-qc/9803077},
year = {2009}
}
Comments
4 pages, RevTeX, to appear in Phys. Rev. Lett., Comments added, refs updated