Hamiltonian formulation of general relativity in the teleparallel geometry- art. no. 084014

We establish a Hamiltonian formulation of the teleparallel equivalent of ge neral relativity, without fixing the time gauge condition, by rigorously pe rforming a Legendre transform. The time gauge condition, previously conside red, 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 struc turally different from the standard Arnowitt-Deser-Misner formulation in ma ny aspects, the main one being that the dynamics is now governed by the Ham iltonian constraint H-o and a set of primary constraints. The vector constr aint H-i is derived from the Hamiltonian constraint. The vanishing of the l atter implies the vanishing of the vector constraint.