Regularized expression for the gravitational energy-momentum in teleparallel gravity and the principle of equivalence

TL;DR

This paper extends the definition of gravitational energy-momentum in teleparallel gravity to arbitrary tetrad fields, addressing reference frames and the principle of equivalence, and proposes a regularized expression for energy-momentum.

Contribution

It introduces a regularized gravitational energy-momentum expression applicable to any tetrad field, clarifying the role of reference frames in teleparallel gravity.

Findings

Extended energy-momentum expression with reference subtraction

Application to Kerr space-time reference frames

Reaffirmed the compatibility of energy-momentum definition with the principle of equivalence

Abstract

The expression of the gravitational energy-momentum defined in the context of the teleparallel equivalent of general relativity is extended to an arbitrary set of real-valued tetrad fields, by adding a suitable reference space subtraction term. The characterization of tetrad fields as reference frames is addressed in the context of the Kerr space-time. It is also pointed out that Einstein's version of the principle of equivalence does not preclude the existence of a definition for the gravitational energy-momentum density.