Static axially symmetric Einstein-Yang-Mills-dilaton solutions. II. Black hole solutions

We discuss the new class of static axially symmetric black hole solutions obtained recently in Einstein-Yang-Mills and Einstein-Yang-Mills-dilaton theory. These black hole solutions are asymptotically flat and they possess a regular event horizon. The event horizon is almost spherically symmetric with a slight elongation along the symmetry axis. The energy density of the matter fields is angle-dependent at the horizon. The static axially symmetric black hole solutions satisfy a simple relation between mass, dilaton charge, entropy and temperature. The black hole solutions are characterized by two integers, the winding number n and the node number k of the purely magnetic gauge field. With increasing node number the magnetically neutral black hole solutions form sequences tending to limiting solutions with magnetic charge n, corresponding to Einstein-Maxwell-dilaton black hole solutions for finite dilaton coupling constant and to Reissner-Nordstrøm black hole solutions for vanishing dilaton coupling constant.