Three dimensional nonlinear magnetic AdS solutions through topological defects

Abstract

Inspired by large applications of topological defects in describing different phenomena in physics, and considering the importance of three dimensional solutions in AdS/CFT correspondence, in this paper we obtain magnetic anti-de Sitter solutions of nonlinear electromagnetic fields. We take into account three classes of nonlinear electrodynamic models; first two classes are the well-known BornInfeld like models including logarithmic and exponential forms and third class is known as the power Maxwell invariant nonlinear electrodynamics. We investigate the effects of these nonlinear sources on three dimensional magnetic solutions. We show that these asymptotical AdS solutions do not have any curvature singularity and horizon. We also generalize the static metric to the case of rotating solutions and find that the value of the electric charge depends on the rotation parameter. Finally, we consider the quadratic Maxwell invariant as a correction of Maxwell theory and we investigate the effects of nonlinearity as a correction. We study the behavior of the deficit angle in presence of these theories of nonlinearity and compare them with each other. We also show that some cases with negative deficit angle exists which are representing objects with different geometrical structure. We also show that in case of the static only magnetic field exists whereas by boosting the metric to rotating one, electric field appears too.

Dynamical and thermal stabilities of nonlinearly charged AdS black holes

“…The behavior of heat capacity could also represent phase transitions [78,79]. By numerical calculation, we have shown the existence of phase transition in Figs.…”

“…C V : which measures the heat capacity when the heat is added to the system keeping the volume constant and C P : which is used when the heat is added at constant pressure. Heat capacities can be calculated using the standard thermodynamic relations [78,79]…”

Thermodynamics and Phase Transition of Topological Dilatonic Lifshitz‐Like Black Holes

“…[ 24,25 ] Although the Quevedo metric solved most of the problems of the previous metrics, it faced a problem in several specific cases. To solve its problem, a new metric has been recently introduced [ 26 ] in which the problem of additional singularities that are not consistent with any of the phase transition points is not observed.…”

“…However, Quevedo metric is not, completely, a successful model in several specific systems and its Ricci scalar has extra divergence point without physical interpretation. Finally, a new metric was proposed [ 26–28 ] in which the problem of mismatched divergency is not observed. [ 29–31 ]…”

Non-perturbative quantum corrections to a Born–Infeld black hole and its information geometry

“…We will also analyze the non-perturbative corrections to the information-theoretical geometry of this system. This will be done using different informational theoretical metrics for this system [52][53][54][55][56][57][58]. It will be observed that these non-perturbative corrections will produce a non-trivial modification to the information-theoretical geometry of this system.…”