Topological aspect of black hole with Skyrme hair

TL;DR

This paper investigates how black holes with Skyrme hair influence baryon charge distribution, revealing fractional charges outside the horizon through topological current analysis in Einstein-Skyrme theory.

Contribution

It introduces a topological current framework to analyze monopole behavior around black holes with Skyrme hair, highlighting fractional baryon charges outside the horizon.

Findings

Fractional baryon charge exists outside the black hole horizon.

Topological current corresponds to monopoles around the black hole.

Branch processes of monopoles are discussed during evolution.

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.