General Relativity on a Null Surface: Hamiltonian Formulation in the Teleparallel Geometry

The Hamiltonian formulation of generalrelativity on a null surface is established in theteleparallel geometry. No particular conditions on thetetrads are imposed, like the time gauge condition. Bymeans of a 3 + 1 decomposition the resultingHamiltonian arises as a completely constrained system.However, it is structurally different from the standardArnowitt–Deser–Misner (adm) typeformulation. In this geometrical framework the basic fieldquantities are tetrads that transform under the globalSO(3, 1) and the torsion tensor.