SELF-GRAVITATING SOLUTIONS OF THE SKYRME MODEL AND THEIR STABILITY

We give a brief survey of the spherically symmetric soliton and black hole solutions of the Einstein-Skyrme system, of which we have present ed the fundamental branches in a recent publication. Some of the basic features and the linear stability properties of both classes of solut ions are discussed. We also derive a mass variation formula for genera l stationary Skyrme black holes and show that the latter assumes the f amiliar vacuum form in the static, spherically symmetric case under co nsideration. We conclude with new results of a numerical non-linear st ability analysis which yields strong evidence for the stability of the fundamental soliton solutions. Thus, contrary to the solutions of the Einstein-Yang-Mills system, all arguments indicate that the Einstein- Skyrme black holes represent stable counter examples to the no-hair co njecture.