# $D$-dimensional charged Anti-de-Sitter black holes in $f(T)$ gravity

## TL;DR

This paper introduces new $D$-dimensional charged Anti-de-Sitter black hole solutions in $f(T)$ gravity with quadratic torsion terms, revealing unique electric potential features, milder singularities, and thermodynamic law violations.

## Contribution

It presents novel charged black hole solutions in $f(T)$ gravity with quadratic torsion, highlighting their unique electric potential structure and thermodynamic properties.

## Key findings

- Existence of inseparable electric monopole and quadrupole terms.
- Milder curvature singularities compared to GR solutions.
- Violation of the first law of thermodynamics.

## Abstract

We present a $D$-dimensional charged Anti-de-Sitter black hole solutions in $f(T)$ gravity, where $f(T)=T+\beta T^2$ and $D \geq 4$. These solutions are characterized by flat or cylindrical horizons. The interesting feature of these solutions is the existence of inseparable electric monopole and quadrupole terms in the potential which share related momenta, in contrast with most of the known charged black hole solutions in General Relativity and its extensions. Furthermore, these solutions have curvature singularities which are milder than those of the known charged black hole solutions in General Relativity and Teleparallel Gravity. This feature can be shown by calculating some invariants of curvature and torsion tensors. Furthermore, we calculate the total energy of these black holes using the energy-momentum tensor. Finally, we show that these charged black hole solutions violate the first law of thermodynamics in agreement with previous results.