ECHOING AND SCALING IN EINSTEIN-YANG-MILLS CRITICAL COLLAPSE

We confirm recent numerical results of echoing and mass scaling in the gravitational collapse of a spherical Yang-Mills field by constructin g the critical solution and its perturbations as an eigenvalue problem . Because the field equations are not scale invariant, the Yang-Mills critical solution is asymptotically, rather than exactly, self-similar , but the methods for dealing with discrete self-similarity developed for the real scalar field can be generalized. We find an echoing perio d Delta = 0.73784 +/- 0.00002 and a critical exponent for the black ho le mass gamma = 0.1964 +/- 0.0007.