Causal Propagation of Constraints and the Canonical Form of General Relativity

Details Causal Propagation of Constraints and the Canonical Form of General Relativity Causal Propagation of Constraints and the Canonical Form of General Relativity

1998-07-22

arxiv.org/abs/gr-qc/9807062v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, no figures, Latex

Scientific paper

Studies of new hyperbolic systems for the Einstein evolution equations show that the ``slicing density'' $\alpha(t,x)$ can be freely specified while the lapse $N = \alpha g^{1/2}$ cannot. Implementation of this small change in the Arnowitt-Deser-Misner action principle leads to canonical equations that agree with the Einstein equations whether or not the constraints are satisfied. The constraint functions, independently of their values, then propagate according to a first order symmetric hyperbolic system whose characteristic cone is the light cone. This result follows from the twice-contracted Bianchi identity and constitutes the central content of the constraint ``algebra'' in the canonical formalism.

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