Hamiltonian time evolution for general relativity. (English) Zbl 0949.83010
Summary: 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 \(\alpha\).
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83C40 | Gravitational energy and conservation laws; groups of motions |
Keywords:
general relativity; Hamiltonian time evolution; Arnowitt-Deser-Misner-Teitelboim-Ashtekar action; twice-contracted Bianchi identityReferences:
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