Asymptotically anti-de Sitter magnetic branes in (n + 1)-dimensional dilaton gravity

Abstract

We present a new class of asymptotically anti-de Sitter (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 space–time with a 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 the dilaton field goes to infinity. We generalized 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 that is proportional to the magnitude of the rotation parameters. Finally, we used the counterterm method inspired by AdS – conformal field theory correspondence and computed the conserved quantities of these space–times. 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.