The generalization of the ADM gravitational energy-momentum

Abstract

In this paper, it is proved that the teleparallel energy-momentum generalizes that of the 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 pseudo-tensor 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.

21 pages

References in corpus (8)

• The teleparallel equivalent of general relativity
• Review of the Hamiltonian analysis in teleparallel gravity
• Hamiltonian formulation of teleparallel gravity
• Is Teleparallel Gravity really equivalent to General Relativity?
• Hamiltonian formulation of unimodular gravity in the teleparallel geometry
• On Conserved Quantities for the Schwarzschild Black Hole in Teleparallel Gravity
• Lorentz symmetries and primary constraints in covariant teleparallel gravity
• Weitzenböck's Torsion, Fermi Coordinates and Adapted Frames

Cited by in corpus (4)

• Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity
• On the gravitational energy problem and the energy of photons
• Conventionalism, cosmology and teleparallel gravity
• Gravitational energy in pp-wave spacetimes