Black Holes with Skyrme Hair
  This paper is intended to give a review of the recent developments on black holes with Skyrme hair. The Einstein-Skyrme system is known to possess black hole solutions with Skyrme hair. The spherically symmetric black hole skyrmion with B=1 was the first discovered counter example of the no-hair conjecture for black holes. Recently we found the B=2 axially symmetric black hole skyrmion. In this system, the black hole at the center of the skyrmion absorbs the baryon number partially, leaving fractional charge outside the horizon. Therefore the baryon number is no longer conserved. We examine the B=1, 2 black hole solutions in detail in this paper. The model has a natural extension to the gauged version which can describe monopole black hole skyrmions. Callan and Witten discussed the monopole catalysis of proton decay within the Skyrme model. We apply the idea to the Einstein-Maxwell-Skyrme system and obtain monopole black hole skyrmions. Remarkably there exist multi-black hole skyrmion solutions in which the gravitational, electromagnetic, and strong forces between the monopoles are all in balance. The solutions turn out to be stable under spherically symmetric linear perturbations. 
Noriko Shiiki and Nobuyuki Sawado