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 presented the fundamental branches in a recent publication. Some of the basic features and the linear stability properties of both classes of solutions are discussed. We also derive a mass variation formula for general stationary Skyrme black holes and show that the latter assumes the familiar vacuum form in the static, spherically symmetric case under consideration. We conclude with new results of a numerical non-linear stability 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 conjecture.