Rotating and non-rotating AdS black holes in $f({\cal T})$ gravity non-linear electrodynamics

TL;DR

This paper derives new exact charged black hole solutions in quadratic teleparallel gravity with non-linear electrodynamics, analyzing their asymptotic behavior, singularities, and thermodynamic properties, revealing deviations from standard entropy-area relations.

Contribution

It presents novel d-dimensional black hole solutions in $f(T)$ gravity with non-linear electrodynamics, including detailed thermodynamic analysis and constraints on parameters.

Findings

Black holes behave asymptotically as AdS solutions.

Entropy is not proportional to the black hole area.

Positive entropy constrains the quadrupole term.

Abstract

We derive new exact charged $d$-dimensional black hole solutions for quadratic teleparallel equivalent gravity, $f({\cal T})=a_0+a_1{\cal T}+a_2{\cal T}^2$, where $\cal T$ is the torsion scalar, in the case of non-linear electrodynamics. We give a specific form of electromagnetic function and find out the form of the unknown functions that characterize the vielbeins in presence of the electromagnetic field. It is possible to show that the black holes behave asymptotically as AdS solutions and contain, in addition to the monopole and quadrupole terms, other higher order terms whose source is the non-linear electrodynamics field. We calculate the electromagnetic Maxwell field and show that our d-dimensional black hole solutions coincide with the previous obtained one \cite{2017JHEP...07..136A}. The structure of the solutions show that there is a central singularity that is much mild in comparison with the respective one in General Relativity. Finally, the thermodynamical properties of the solutions are investigated by calculating the entropy, the Hawking temperature, the heat capacity, and other physical quantities. The most important result of thermodynamics is that the entropy is not proportional to the area of the black hole. This inanition points out that we must have a constrain on the quadrupole term to get a positive entropy otherwise we get a negative value.