Hamiltonian Time Evolution for General Relativity

Details Hamiltonian Time Evolution for General Relativity Hamiltonian Time Evolution for General Relativity

1998-07-16

arxiv.org/abs/gr-qc/9807041v1

Phys.Rev.Lett. 81 (1998) 1154-1157

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages, revtex, to appear in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.81.1154

Hamiltonian time evolution in terms of an explicit parameter time is derived for general relativity, even when the constraints are not satisfied, from the Arnowitt-Deser-Misner-Teitelboim-Ashtekar action in which the slicing density $\alpha(x,t)$ is freely specified while the lapse $N=\alpha g^{1/2}$ is not. The constraint ``algebra'' becomes a well-posed evolution system for the constraints; this system is the twice-contracted Bianchi identity when $R_{ij}=0$. The Hamiltonian constraint is an initial value constraint which determines $g^{1/2}$ and hence $N$, given $\alpha$.

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