STATIC SPHERICALLY SYMMETRICAL SOLUTIONS OF THE EINSTEIN-YANG-MILLS EQUATIONS

We study the global behaviour of static, spherically symmetric solutions of the Einstein-Yang-Mills equations with gauge group SU(2). Our analysis results in three disjoint classes of solutions with a regular origin or a horizon. The 3-spaces (t = const.) of the first, generic class are compact and singular. The second class consists of an infinite family of globally regular, resp. black hole solutions. The third type is an oscillating solution, which although regular is not asymptotically flat.