Magnetic brane solutions of Lovelock gravity with nonlinear electrodynamics

TL;DR

This paper explores magnetic brane solutions in Lovelock gravity coupled with nonlinear electrodynamics, revealing their geometric properties, effects of gravity terms, and extensions to rotating cases in higher dimensions.

Contribution

It introduces new magnetic brane solutions with nonlinear electrodynamics in Lovelock gravity, analyzing their singularity structure, conic deficits, and conserved quantities, including rotating extensions.

Findings

Solutions lack curvature singularities and horizons.

Lovelock gravity terms do not influence the deficit angle.

Rotating solutions and their conserved quantities are derived.

Abstract

In this paper, we consider logarithmic and exponential forms of nonlinear electrodynamics as a source and obtain magnetic brane solutions of the Lovelock gravity. Although these solutions have no curvature singularity and no horizon, they have a conic singularity with a deficit angle. We investigate the effects of nonlinear electrodynamics and the Lovelock gravity on the value of deficit angle and find that various terms of Lovelock gravity do not affect deficit angle. Next, we generalize our solutions to spinning cases with maximum rotating parameters in arbitrary dimensions and calculate the conserved quantities of the solutions. Finally, we consider nonlinear electrodynamics as a correction of the Maxwell theory and investigate the properties of the solutions.