Charged Black Holes in Generalized Teleparallel Gravity

TL;DR

This paper explores charged black hole solutions in generalized teleparallel gravity, deriving new solutions and analyzing the applicability of common gauges, with implications for nonlinear models and no-go theorems.

Contribution

It introduces non-diagonal tetrads in teleparallel gravity, derives solutions for nonlinear models, and examines gauge applicability and no-go theorems in this framework.

Findings

Reobtained RN-AdS solution for linear f(T)

Identified limitations of Schwarzschild gauge in nonlinear cases

Analyzed a no-go theorem in modified teleparallel gravity

Abstract

In this paper we investigate charged static black holes in 4D for generalized teleparallel models of gravity, based on torsion as the geometric object for describing gravity according to the equivalence principle. As a motivated idea, we introduce a set of non-diagonal tetrads and derive the full system of non linear differential equations. We prove that the common Schwarzschild gauge is applicable only when we study linear f(T) case. We reobtain the Reissner-Nordstrom-de Sitter (or RN-AdS) solution for the linear case of f(T) and perform a parametric cosmological reconstruction for two nonlinear models. We also study in detail a type of the no-go theorem in the framework of this modified teleparallel gravity.