Abstract. Considering the nonlinear electromagnetic field coupled to Einstein gravity in the presence of a 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 δ. 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 constraint on the nonlinear parameter, such that the nonlinear electromagnetic field is conformally invariant.

PACS numbers: 04.50.−h, 04.20.Jb, 04.40.Nr

Print publication: Issue 22 (21 November 2009)
Received 12 May 2009, in final form 7 September 2009
Published 23 October 2009