Self-gravitating Yang monopoles in all dimensions

The ( 2k + 2)-dimensional Einstein-Yang-Mills equations for gauge group SO( 2k) ( or SU( 2) for k = 2 and SU( 3) for k = 3) are shown to admit a family of spherically symmetric magnetic monopole solutions, for both zero and nonzero cosmological constant Lambda, characterized by a mass m and a magnetic-type charge. The k = 1 case is the Reissner-Nordstrom black hole. The k = 2 case yields a family of self-gravitating Yang monopoles. The asymptotic spacetime is Minkowski for Lambda = 0 and anti-de Sitter for Lambda < 0, but the total energy is infinite for k > 1. In all cases, there is an event horizon when m > m(c), for some critical mass mc, which is negative for k > 1. The horizon is degenerate when m = mc, and the near-horizon solution is then an AdS(2) x S-2k vacuum.