Hamiltonian formulation of general relativity in the teleparallel geometry

J. W. Maluf and J. F. da Rocha-Neto
Phys. Rev. D 64, 084014 – Published 24 September 2001
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Abstract

We establish a Hamiltonian formulation of the teleparallel equivalent of general relativity, without fixing the time gauge condition, by rigorously performing a 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 four-dimensional space-time. The resulting Hamiltonian formulation is structurally different from the standard Arnowitt-Deser-Misner formulation in many aspects, the main one being that the dynamics is now governed by the Hamiltonian constraint H0 and a set of primary constraints. The vector constraint Hi is derived from the Hamiltonian constraint. The vanishing of the latter implies the vanishing of the vector constraint.

  • Received 16 March 2001

DOI:https://doi.org/10.1103/PhysRevD.64.084014

©2001 American Physical Society

Authors & Affiliations

J. W. Maluf* and J. F. da Rocha-Neto

  • Instituto de Física, Universidade de Brasília, C.P. 04385, 70.919-970 Brasília, DF Brazil

  • *Email address: wadih@fis.unb.br

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Issue

Vol. 64, Iss. 8 — 15 October 2001

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