The general expression for $f(T)$ in a charged cylindrical spacetime with diverse dimensions

Abstract

By utilizing the field equations of the modified teleparallel equivalent of general relativity, denoted as $\mathit{f(T)}$, we obtain an exact solution for a static charged black hole in n-dimensions, without imposing any constraints. The black hole possesses two distinctive dimensional constants: $m$ and $v$ with unit {\textit length}. The first constant is associated with the mass, while the second constant represents the electric charge. The existence of this electrical charge causes the black hole to diverge from the expectations of the teleparallel equivalent of general relativity (TEGR). Our analysis demonstrates that $\mathit{f(T)}$ is reliant on the parameter $v$ and transforms into a constant expression when $v$ is assigned a value of zero. A captivating aspect of this particular black hole is its absence of singularities in the quantities formed using torsion and curvature, given that the dimension $n$ falls within the interval of $4 \leq n \leq 6$ as $r$ approaches zero. However, for $n\geq7$, the singularity becomes milder in comparison to the case of TEGR. Furthermore, By utilizing the conserved n-momentum vector, we calculate the energy of this solution and confirm its correspondence with the ADM mass, accurate to the order of $O\Big(\frac{1}{r}\Big)$. Otherwise, we observe higher-order contributions arising from the electric charge terms. Through the application of a coordinate transformation to the black hole, we derive a precise solution describing a stationary rotating black hole. This solution showcases significant readings of the torsion scalar and the analytical function $\mathit{f(T)}$. In order to gain insight into the physics of this black hole, we calculate various physical quantities related to thermodynamics, such as entropy, Hawking temperature, and heat capacity. The analysis reveals that the black hole exhibits thermal stability.