Three dimensional nonlinear magnetic AdS solutions through topological defects

TL;DR

This paper explores three-dimensional AdS magnetic solutions with nonlinear electromagnetic fields, analyzing their properties, effects of nonlinearity, and the impact of rotation, revealing non-singular, horizonless geometries with varied deficit angles.

Contribution

It introduces new three-dimensional magnetic AdS solutions with nonlinear electrodynamics, including rotating cases and effects of nonlinearity as corrections to Maxwell theory.

Findings

Solutions are free of curvature singularities and horizons.

Rotation induces electric fields in static magnetic solutions.

Nonlinearity affects the deficit angle and geometric structure.

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 in other words, 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 appear too.