https://doi.org/10.1140/epjc/s10052-019-7424-x
Regular Article - Theoretical Physics
Rotating and non-rotating AdS black holes in
gravity non-linear electrodynamics
1
Dipartimento di Fisica “E. Pancini“, Universitá di Napoli “Federico II”, Complesso Universitario di Monte Sant’ Angelo, Edificio G, Via Cinthia, 80126, Naples, Italy
2
Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli, Complesso Universitario di Monte Sant’Angelo, Edificio G, Via Cinthia, 80126, Naples, Italy
3
Gran Sasso Science Institute, Viale F. Crispi, 7, 67100, L’Aquila, Italy
4
Laboratory for Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050, Tomsk, Russia
5
Centre for Theoretical Physics, The British University in Egypt, P.O. Box 43, El Shorouk, 11837, Cairo, Egypt
6
Mathematics Department, Faculty of Science, Ain Shams University, Cairo, 11566, Egypt
* e-mail: nashed@bue.edu.eg
Received:
23
August
2019
Accepted:
19
October
2019
Published online:
11
November
2019
We derive new exact charged d-dimensional black hole solutions for quadratic teleparallel equivalent gravity, , where
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 (Awad et al. in J High Energy Phys 13:1706.01773, 2017). 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.
© The Author(s), 2019