Spacetimes with Longitudinal and Angular Magnetic Fields in Third Order Lovelock Gravity

TL;DR

This paper introduces two new classes of magnetic brane solutions in third order Lovelock gravity, including static and spinning cases with longitudinal and angular magnetic fields, analyzing their properties and conserved quantities.

Contribution

The paper presents novel magnetic brane solutions in third order Lovelock gravity, including spinning and static cases with unique geometric and charge properties.

Findings

Solutions have no curvature singularities or horizons.

Spinning branes acquire electric charge proportional to rotation.

Conserved quantities are computed using the counterterm method.

Abstract

We obtain two new classes of magnetic brane solutions in third order Lovelock gravity. The first class of solutions yields an $(n+1)$-dimensional spacetime with a longitudinal magnetic field generated by a static source. We generalize this class of solutions to the case of spinning magnetic branes with one or more rotation parameters. These solutions have no curvature singularity and no horizons, but have a conic geometry. For the spinning brane, 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, while the static brane has no net electric charge. The second class of solutions yields a pacetime with an angular magnetic field. These solutions have no curvature singularity, no horizon, and no conical singularity. Although the second class of solutions may be made electrically charged by a boost transformation, the transformed solutions do not present new spacetimes. Finally, we use the counterterm method in third order Lovelock gravity and compute the conserved quantities of these spacetimes.