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Spacetimes with longitudinal and angular magnetic fields in third order Lovelock gravity

We obtain two new classes of magnetic 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 strings with one or more rotation parameters. These solutions have no curvature singularity and no horizons, but have a conic geometry. For the spinning string, when one or more rotation parameters are nonzero, the string has a net electric charge which is proportional to the magnitude of the rotation parameters, while the static string has no net electric charge. 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. 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.