Spherically symmetric charged black hole in conformal teleparallel equivalent of general relativity

TL;DR

This paper investigates spherically symmetric black hole solutions within conformal teleparallel gravity, demonstrating that Schwarzschild and Reissner-Nordström solutions are unique in this framework, with the scalar field having no effect.

Contribution

It identifies the unique black hole solutions in conformal teleparallel gravity and shows the scalar field's non-effect on spherically symmetric spacetimes.

Findings

Schwarzschild and Reissner-Nordström are the only solutions.

Scalar field does not influence spherically symmetric spacetimes.

Derived non-linear differential equations for the solutions.

Abstract

We study 4-dimensional non-charged and charged spherically symmetric spacetimes in conformal teleparallel equivalent of general relativity. We apply the gravitational field equations in non-charged and charged spacetimes to the diagonal and non-diagonal vierbeins and derive their sets of the non-linear differential equations. It is demonstrated that the Schwarzschild, for the non-charged case, and the Reissner-Nordstr\"om, for the charged case, are the only black hole solutions for the spherically symmetric case in the framework of the conformal teleparallel equivalent of general relativity theory. As a result, it is found that in the conformal teleparallel equivalent of general relativity theory, the scalar field cannot have any effect for the spherically symmetric manifold.