Reissner Nordstr$\ddot{o}$m solutions and Energy in teleparallel theory

TL;DR

This paper explores Reissner-Nordström black hole solutions within the teleparallel theory of gravitation, analyzing their energy content and the conditions affecting energy calculations at infinity.

Contribution

It presents three spherically symmetric solutions with electromagnetic fields in teleparallel gravity, including an arbitrary function, and examines their energy using the superpotential method.

Findings

Energy depends on the decay rate of tetrad components at infinity.

Different energy results are obtained unless specific fall-off conditions are met.

The solutions generalize the Reissner-Nordström black hole in teleparallel gravity.

Abstract

We give three different spherically symmetric spacetimes for the coupled gravitational and electromagnetic fields with charged source in the tetrad theory of gravitation. One of these, contains an arbitrary function and generates the others. These spacetimes give the Reissner Nordstr$\ddot{o}$m metric black hole. We then, calculated the energy associated with these spacetimes using the superpotential method. We find that unless the time-space components of the tetrad field go to zero faster than ${1/\sqrt{r}}$ at infinity, one gets different results for the energy.