  We study various aspects of black holes and gravitational collapse in
Einstein-Yang-Mills theory under the assumption of spherical symmetry.
Numerical evolution on hyperboloidal surfaces extending to future null infinity
is used. We begin by constructing colored and Reissner-Nordstrom black holes on
surfaces of constant mean curvature and analyze their perturbations. These
linearly perturbed black holes are then evolved into the nonlinear regime and
the masses of the final Schwarzschild black holes are computed as a function of
the initial horizon radius. We compare with an information-theoretic bound on
the lifetime of unstable hairy black holes derived by Hod. Finally we study
critical phenomena in gravitational collapse at the threshold between different
Yang-Mills vacuum states of the final Schwarzschild black holes, where the n=1
colored black hole forms the critical solution. The work of Choptuik et al.
(1999) is extended by using a family of initial data that includes another
region in parameter space where the colored black hole with the opposite sign
of the Yang-Mills potential forms the critical solution. We investigate the
boundary between the two regions and discover that the Reissner-Nordstrom
solution appears as a new approximate codimension-two attractor.
