Asymptotically AdS Magnetic Branes in (n+1)-dimensional Dilaton Gravity

TL;DR

This paper introduces a new class of asymptotically AdS magnetic solutions in higher-dimensional dilaton gravity, featuring conic geometries with no singularities or horizons, and explores their properties including rotation and conserved quantities.

Contribution

The work presents novel asymptotically AdS magnetic brane solutions in higher dimensions with Liouville potentials, including rotating cases and analysis of their conserved charges.

Findings

Solutions are free of curvature singularities and horizons.

Rotating solutions acquire a net electric charge proportional to rotation.

Conserved quantities are independent of the dilaton field.

Abstract

We present a new class of asymptotically AdS magnetic solutions in ($n+1$)-dimensional dilaton gravity in the presence of an appropriate combination of three Liouville-type potentials. This class of solutions is asymptotically AdS in six and higher dimensions and yields a spacetime with longitudinal magnetic field generated by a static brane. These solutions have no curvature singularity and no horizons but have a conic geometry with a deficit angle. We find that the brane tension depends on the dilaton field and approaches a constant as the coupling constant of dilaton field goes to infinity. 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. Finally, we use the counterterm method inspired by AdS/CFT correspondence and compute the conserved quantities of these spacetimes. We found that the conserved quantities do not depend on the dilaton field, which is evident from the fact that the dilaton field vanishes on the boundary at infinity.