Magnetic Branes Supported by Nonlinear Electromagnetic Field

TL;DR

This paper introduces new higher-dimensional magnetic brane solutions in Einstein gravity coupled with nonlinear electromagnetic fields, analyzing their geometric properties, effects of nonlinearity, and conserved quantities, including the impact of rotation and conformal invariance constraints.

Contribution

It presents novel magnetic brane solutions with nonlinear electromagnetic fields, explores their geometric and physical properties, and extends them to rotating cases with conserved charge calculations.

Findings

Solutions have no curvature singularity or horizons.

Nonlinearity affects the metric function and deficit angle.

Rotating solutions acquire a net electric charge proportional to rotation.

Abstract

Considering the nonlinear electromagnetic field coupled to Einstein gravity in the presence of cosmological constant, we obtain a new class of $d$-dimensional magnetic brane solutions. This class of solutions yields a spacetime with a longitudinal nonlinear magnetic field generated by a static source. These solutions have no curvature singularity and no horizons but have a conic geometry with a deficit angle $\delta \phi$. We investigate the effects of nonlinearity on the metric function and deficit angle and also find that for the special range of the nonlinear parameter, the solutions are not asymptotic AdS. We generalize this class of solutions to the case of spinning magnetic solutions, and find that when one or more rotation parameters are nonzero, the brane has a net electric charge which is proportional to the magnitude of the rotation parameters. Then, we use the counterterm method and compute the conserved quantities of these spacetimes. Finally, we obtain a constrain on the nonlinear parameter, such that the nonlinear electromagnetic field is conformally invariant.