Energy and momentum of a spherically symmetric dilaton frame as regularized by teleparallel gravity

TL;DR

This paper calculates the energy and momentum of a spherically symmetric dilaton frame using teleparallel gravity, showing it provides physically relevant results by accounting for inertia effects and gauge connections.

Contribution

It demonstrates how teleparallel gravity, with a covariant formulation, yields consistent energy-momentum results for dilaton frames, unlike traditional Riemannian approaches.

Findings

Teleparallel gravity yields physically relevant energy-momentum values.

Inertia effects influence total energy and momentum calculations.

Covariant teleparallel formulation corrects discrepancies from Riemannian methods.

Abstract

We calculate energy and momentum of a spherically symmetric dilaton frame using the gravitational energy-momentum 3-form within the tetrad formulation of general relativity (GR). The frame we use is characterized by an arbitrary function $\Upsilon$ with the help of which all the previously found solutions can be reproduced. We show how the effect of inertia {\it (which is mainly reproduced from $\Upsilon$)} makes the total energy and momentum always different from the well known result when we use the Riemannian connection ${{\widetilde \Gamma}_\alpha}^\beta$. On the other hand, when use is made of the covariant formulation of teleparallel gravity, which implies to take into account the pure gauge connection, teleparallel gravity always yields the physically relevant result for the energy and momentum.