Generalization of the ADM gravitational energy momentum

In this paper, it is proved that the teleparallel energy momentum generalizes that of the Arnowitt-Deser-Misner (ADM) formalism. In doing so, it is shown that the teleparallel 4-momentum can be made to coincide with that of the ADM approach whenever the ADM 4-momentum is applicable. The only assumptions are the time gauge for the teleparallel frame and the well-known restrictions for the coordinate system used in the calculation of the ADM 4-momentum. Then, examples where the ADM formalism fails to give consist results, but the teleparallel approach does not, are given. The advantages of the teleparallel stress-energy tensor (density) over the pseudotensor of Landau-Lifshitz are exhibited. Finally, the difficulties in identifying the gravitational angular-momentum density is discussed; it is shown that the spatial part of the proposed angular-momentum density $M^{ab}$ vanishes when the teleparallel frame satisfies the time-gauge condition.