Gravitational Energy-Momentum Density in Teleparallel Gravity
V. C. de Andrade, L. C. T. Guillen, J. G. Pereira
TL;DR
This paper derives a covariant, gauge-invariant energy-momentum density for gravity within teleparallel gravity, aligning with Einstein's theory and Møller's canonical energy-momentum, advancing gravitational energy localization.
Contribution
It introduces a true spacetime and gauge tensor for gravitational energy-momentum in teleparallel gravity, unifying gauge theory and Einstein's equations.
Findings
Derived a conserved energy-momentum gauge current for gravity.
Showed the gauge current reduces to Møller's canonical density.
Reformulated gravitational field equations in a spacetime-covariant form.
Abstract
In the context of a gauge theory for the translation group, a conserved energy-momentum gauge current for the gravitational field is obtained. It is a true spacetime and gauge tensor, and transforms covariantly under global Lorentz transformations. By rewriting the gauge gravitational field equation in a purely spacetime form, it becomes the teleparallel equivalent of Einstein's equation, and the gauge current reduces to the M{\o}ller's canonical energy-momentum density of the gravitational field.
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