Hamiltonian formulation of general relativity in the teleparallel geometry

Details Hamiltonian formulation of general relativity in the teleparallel geometry Hamiltonian formulation of general relativity in the teleparallel geometry

2000-02-16

arxiv.org/abs/gr-qc/0002059v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, Latex file, no figures. The title has been changed. The complete constraint algebra is presented. The derivation of

Scientific paper

10.1103/PhysRevD.64.084014

We establish the Hamiltonian formulation of the teleparallel equivalent of general relativity, without fixing the time gauge condition, by rigorously performing the Legendre transform. The time gauge condition, previously considered, restricts the teleparallel geometry to the three-dimensional spacelike hypersurface. Geometrically, the teleparallel geometry is now extended to the four-dimensional space-time. The resulting Hamiltonian formulation is different from the standard ADM formulation in many aspects, the main one being that the dynamics is now governed by the Hamiltonian constraint H_0 and a set of primary constraints. The vector constraint H_i is derived from the Hamiltonian constraint. The vanishing of the latter implies the vanishing of the vector constraint.

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