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

Abstract

We derive new exact charged $d$-dimensional black hole solutions for quadratic teleparallel equivalent gravity, $f(\mathcal{T})=a_0+a_1\mathcal{T}+a_2{\mathcal{T}}^2$, where $\mathcal{T}$ 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.

14 Pages, 3 Ligures, Latex, Will appear in EPJC

References in corpus (26)

• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• The teleparallel equivalent of general relativity
• On Born-Infeld Gravity in Weitzenbock spacetime
• f(T) gravity mimicking dynamical dark energy. Background and perturbation analysis
• $f(T,\mathcal{T})$ gravity and cosmology
• Good and bad tetrads in f(T) gravity
• Solar system constraints on f(T) gravity
• Observational information for f(T) theories and Dark Torsion
• Static Solutions with Spherical Symmetry in f(T) Theories
• Exact charged black-hole solutions in D-dimensional f(T) gravity: torsion vs curvature analysis
• Weak-Field Spherically Symmetric Solutions in $f(T)$ gravity
• Regular Multi-Horizon Black Holes in Modified Gravity with Non-Linear Electrodynamics
• Model-Independent Distance Measurements from Gamma-Ray Bursts and Constraints on Dark Energy
• Translation of Einstein's Attempt of a Unified Field Theory with Teleparallelism
• Phase transition of quantum corrected Schwarzschild black hole
• Thermodynamics of regular black hole
• A special exact spherically symmetric solution in f(T) gravity theories
• Black holes thermodynamics to all orders in the Planck length in extra dimensions
• Self-Gravitating Spherically Symmetric Solutions in Scalar-Torsion Theories
• FRW in quadratic form of $f(T)$ gravitational theories
• Stationary Axisymmetric Solutions and their Energy Contents in Teleparallel Equivalent of Einstein Theory
• $D$-dimensional charged Anti-de-Sitter black holes in $f(T)$ gravity
• A type of Born-Infeld regular gravity and its cosmological consequences
• Schwarzschild solution in extended teleparallel gravity
• Kerr geometry in f(T) gravity
• Born-Infeld and Charged Black Holes with non-linear source in $f(T)$ Gravity

Cited by in corpus (7)

• Study of gravastars under $f(\mathbb{T})$ gravity
• Testing Born-Infeld $f(T)$ teleparallel gravity through Sgr A${}^{\star }$ observations
• Charged $AdS$ Black Holes in $4D$ Einstein--Gauss--Bonnet Massive Gravity
• Black holes and regular black holes in coincident $f(\mathbb{Q},{\mathbb{B}}_Q)$ gravity coupled to nonlinear electrodynamics
• On "Rotating charged AdS solutions in quadratic $f(T)$ gravity": New rotating solutions
• Kerr-Schild metrics in teleparallel gravity
• Cylindrically symmetric static $n$-dimensional (un)charged (anti-)de Sitter black holes in generic $f(T)$ gravity