# Charged (A)dS black hole solutions in conformal teleparallel equivalent of general relativity

## TL;DR

This paper derives charged and non-charged (Anti)-de Sitter black hole solutions within conformal teleparallel gravity, showing they match those in standard teleparallel equivalent of general relativity and highlighting the scalar field's limited influence.

## Contribution

It presents new black hole solutions in conformal teleparallel gravity and demonstrates their equivalence to solutions in teleparallel equivalent of general relativity.

## Key findings

- Solutions are identical to those in teleparallel equivalent theory.
- Scalar field must be unity for well-known asymptotic spacetime.
- Scalar field does not influence spherical symmetry manifold.

## Abstract

We continue our study in 4-dimension to derive non-charged and charged (Anti)-de Sitter black hole solutions in conformal teleparallel equivalent of general relativity. The non-charged and charged equations of motion are applied to a spherically symmetric tetrad and the non-linear differential equations are derived. It is shown that the output solutions of the two cases are identical to those obtained in teleparallel equivalent theory to general relativity. As a result, it is found that in the conformal teleparallel equivalent theory to general relativity, the scalar field cannot influence on the manifold of spherical symmetry, i.e. the scalar field must equal 1 in order to have a well known asymptote spacetime.