Can the power Maxwell nonlinear electrodynamics theory remove the singularity of electric field of point-like charges at their locations?

YES! We introduce a variable power Maxwell nonlinear electrodynamics theory which can remove the singularity of electric field of point-like charges at their locations. One of the main problems of Maxwell's electromagnetic field theory is related to the existence of singularity for electric field of point-like charges at their locations. In other words, the electric field of a point-like charge diverges at the charge location which leads to an infinite self-energy. In order to remove this singularity a few nonlinear electrodynamics (NED) theories have been introduced. Born-Infeld (BI) NED theory is one of the most famous of them. However the power Maxwell (PM) NED cannot remove this singularity. In this paper, we show that the PM NED theory can remove this singularity, when the power of PM NED is less than $s<\frac{1}{2}$.Comment: 5 pages, 2 figures, accepted in Europhysics Letters (EPL

Einstein-Born-Infeld-Massive Gravity: adS-Black Hole Solutions and their Thermodynamical properties

In this paper, we study massive gravity in the presence of Born-Infeld nonlinear electrodynamics. First, we obtain metric function related to this gravity and investigate the geometry of the solutions and find that there is an essential singularity at the origin ($r=0$). It will be shown that due to contribution of the massive part, the number, types and places of horizons may be changed. Next, we calculate the conserved and thermodynamic quantities and check the validation of the first law of thermodynamics. We also investigate thermal stability of these black holes in context of canonical ensemble. It will be shown that number, type and place of phase transition points are functions of different parameters which lead to dependency of stability conditions to these parameters. Also, it will be shown how the behavior of temperature is modified due to extension of massive gravity and strong nonlinearity parameter. Next, critical behavior of the system in extended phase space by considering cosmological constant as pressure is investigated. A study regarding neutral Einstein-massive gravity in context of extended phase space is done. Geometrical approach is employed to study the thermodynamical behavior of the system in context of heat capacity and extended phase space. It will be shown that GTs, heat capacity and extended phase space have consistent results. Finally, critical behavior of the system is investigated through use of another method. It will be pointed out that the results of this method is in agreement with other methods and follow the concepts of ordinary thermodynamics.Comment: 19 pages with 17 figures, Sections V, VI, VII, VIII with related figures and discussions are added. arXiv admin note: text overlap with arXiv:1507.0656

Magnetic branes in Gauss-Bonnet gravity with nonlinear electrodynamics: correction of magnetic branes in Einstein-Maxwell gravity

In this paper, we are considering two first order corrections to both gravity and gauge sides of the Einstein-Maxwell gravity: Gauss-Bonnet gravity and quadratic Maxwell invariant as corrections. We obtain horizonless magnetic solutions by implying a metric which representing a topological defect. We analyze the geometric properties of the solutions and investigate the effects of both corrections, and find that these solutions may be interpreted as the magnetic branes. We study the singularity condition and find a nonsingular spacetime with a conical geometry. We also investigate the effects of different parameters on deficit angle of spacetime near the origin.Comment: 10 pages with 9 figure

Three-dimensional AdS black holes in massive-power-Maxwell theory

Recently, it was shown that the power-Maxwell (PM) theory could remove the singularity of the electric field (B. Eslam Panah, Europhys. Lett. 134, 20005 (2021)). Motivated by a great interest in three-dimensional black holes and a surge of success in studying massive gravity from both the cosmological and astrophysical points of view, we investigate three-dimensional black hole solutions in de Rham, Gabadadze, and Tolley massive theory of gravity in the presence of PM electrodynamics. First, we extract exact three-dimensional solutions in this theory of gravity. Then we study the geometrical properties of these solutions. Calculating conserved and thermodynamic quantities, we check the validity of the first law of thermodynamics for these black holes. We also examine the stability of these black holes in the context of the canonical ensemble. We continue calculating this kind of black hole’s optical features, such as the photon orbit radius, the energy emission rate, and the deflection angle. Considering these optical quantities, finally, we analyze the effective role of the parameters of models on them.BEP thanks the University of Mazandaran. Also AR acknowledges Universidad de Tarapacá for financial support. AR acknowledges financial support from the Generalitat Valenciana through PROMETEO PROJECT CIPROM/2022/13. A. R. is fund by the María Zambrano contract ZAMBRANO 21-25 (Spain)

Geometrical Method for Thermal Instability of Nonlinearly Charged BTZ Black Holes

We consider three-dimensional BTZ black holes with three models of nonlinear electrodynamics as source. Calculating heat capacity, we study the stability and phase transitions of these black holes. We show that Maxwell, logarithmic, and exponential theories yield only type one phase transition which is related to the root(s) of heat capacity, whereas, for correction form of nonlinear electrodynamics, heat capacity contains two roots and one divergence point. Next, we use geometrical approach for studying classical thermodynamical behavior of the system. We show that Weinhold and Ruppeiner metrics fail to provide fruitful results and the consequences of the Quevedo approach are not completely matched to the heat capacity results. Then, we employ a new metric for solving this problem. We show that this approach is successful and all divergencies of its Ricci scalar and phase transition points coincide. We also show that there is no phase transition for uncharged BTZ black holes