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

Understand

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.