Magnetic Branes in Gauss-Bonnet Gravity

TL;DR

This paper introduces new magnetic brane solutions in Einstein-Maxwell-Gauss-Bonnet gravity with negative cosmological constant, revealing their geometric properties, electric charge behavior, and conserved quantities.

Contribution

The paper presents novel static and spinning magnetic brane solutions in Gauss-Bonnet gravity, including their geometric features and charge characteristics, extending previous models.

Findings

Solutions have no curvature singularity or horizons

Spinning branes acquire electric charge proportional to rotation

Conserved quantities are computed using the counterterm method

Abstract

We present two new classes of magnetic brane solutions in Einstein-Maxwell-Gauss-Bonnet gravity with a negative cosmological constant. The first class of solutions yields an $(n+1)$-dimensional spacetime with a longitudinal magnetic field generated by a static magnetic brane. We also generalize this solution to the case of spinning magnetic branes with one or more rotation parameters. We find that these solutions have no curvature singularity and no horizons, but have a conic geometry. In these spacetimes, when all the rotation parameters are zero, the electric field vanishes, and therefore the brane has no net electric charge. For the spinning brane, when one or more rotation parameters are non zero, the brane has a net electric charge which is proportional to the magnitude of the rotation parameter. The second class of solutions yields a spacetime with an angular magnetic field. These solutions have no curvature singularity, no horizon, and no conical singularity. Again we find that the net electric charge of the branes in these spacetimes is proportional to the magnitude of the velocity of the brane. Finally, we use the counterterm method in the Gauss-Bonnet gravity and compute the conserved quantities of these spacetimes.