Energy of spherically symmetric spacetimes on regularizing teleparallelism

TL;DR

This paper compares different formulations of teleparallel gravity to accurately compute the energy of spherically symmetric spacetimes, highlighting the importance of covariant approaches to avoid unphysical results.

Contribution

It demonstrates how the covariant teleparallel approach yields physically meaningful energy calculations for spherically symmetric solutions, unlike traditional methods affected by inertial effects.

Findings

Covariant teleparallelism provides consistent energy values.

Inertial effects can lead to unphysical energy results in non-covariant formulations.

Momentum calculations remain unaffected by inertial effects.

Abstract

We calculate the total energy of an exact spherically symmetric solutions, i.e., Schwarzschild and Reissner Nordstr$\ddot{o}$m, using the gravitational energy-momentum 3-form within the tetrad formulation of general relativity. We explain how the effect of the inertial makes the total energy unphysical! Therefore, we use the covariant teleparallel approach which makes the energy always physical one. We also show that the inertial has no effect on the calculation of momentum.