Topological aspect of black hole with Skyrme hair

Abstract

Based on the $\phi$-mapping topological current theory, we show that the presence of the black hole leaves fractional baryon charge outside the horizon in the Einstein-Skyrme theory. A topological current is derived from the Einstein-Skyrme system, which corresponds to the monopoles around the black hole. The branch process (splitting, merging and intersection) is simply discussed during the evolution of the monopoles.