Stable Black Hole with Yang-Mills Hair

Abstract: We present stable solution of static spherically symmetric Einstein-Yang-Mills equations with the SU(2) gauge group. This solution is asymptotically flat and regular at r = 0 and with nontrivial Yang-Mills(YM) connection. With quantized values of the Arnowitt-Deser-Misner (ADM) mass, the solutions asymptotically approach the Schwarzschild solution and have zero global YM charges. Numerical evidences suggest that this solution is both linearly and nonlinearly stable and has a ring of generic curvature singularities along the horizon. An effective counterexample to the no-hair conjecture is provided by this stable solution. Moreover, the stable black hole solution suggests that the coupling of gauge field to gravity in early Universe will generate a new type of black holes. Their stability means that these might be a possible new source of primordial black holes left over from the early Universe and serves as a possible new candidate for dark matter.