Teleparallel Gravity and the Gravitational Energy-Momentum Density

In the context of the teleparallel equivalent of general relativity, we show that the energy-momentum density for the gravitational field can be described by a true spacetime tensor. It is also invariant under local (gauge) translations of the tangent space coordinates, but transforms covariantly only under global Lorentz transformations. When the gauge gravitational field equation is written in a purely spacetime form, it becomes the teleparallel equivalent of Einstein’s equation, and we recover M{\o}ller’s expression for the canonical gravitational energy-momentum pseudotensor.