Infinitely coloured black holes

We formulate the field equations for SU(infinity) Einstein-Yang-Mills theor y, and use an analytic approximation to elucidate the properties of spheric ally symmetric black hole solutions. This model may be motivated by string theory considerations, given the enormous gauge symmetries which characteri ze string theory. The solutions simplify considerably in the presence of a negative cosmological constant, particularly for the limiting cases of a ve ry large cosmological constant or very small gauge field. The black holes p ossess infinite amounts of gauge field hair, and we speculate on possible c onsequences of this for quantum decoherence, which, however, we do not tack le here.