The general expression for [formula omitted] in a charged cylindrical spacetime with diverse dimensions

Abstract

By utilizing the field equations of the modified teleparallel equivalent of general relativity, denoted as 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 length. The first constant is associated with the mass, while the second constant represents the electric charge. The presence of this electric charge leads the black hole to deviate from the predictions of the teleparallel equivalent of general relativity (TEGR). We show that f(T) depends on the constant v and becomes a constant function when v is set to zero. An intriguing feature of this black hole is its lack of singularities in the invariants built from torsion and curvature when the dimension n lies within the range of 4≤n≤6 as r→0. However, for n≥7, the singularity becomes milder in comparison to the case in the teleparallel equivalent of general relativity (TEGR). Furthermore, we compute the energy of this solution using the conserved n-momentum vector and establish its equivalence to the ADM mass, up to O(1r). Otherwise, we observe higher-order contributions arising from the electric charge terms. By performing a coordinate transformation on the black hole, we obtain an exact solution for a stationary rotating black hole, which exhibits non-trivial values of the torsion scalar and the analytic function 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.