Hairy black hole solutions to \(SU(3)\) Einstein-Yang-Mills equations (Q5956420)

In this paper a rigorous proof of the existence of infinitely many black hole solutions to the Einstein-Yang-Mills equations with gauge group SU(3) is given. It is implied by this theorem that at infinity, the field is constant and the spacetime metric is that of the one. It is also shown that each of these solutions has a finite ADM mass m, which is derived from the solution, not an arbitrary constant. In this paper the notion of crashing, connecting and exiting trajectories on the plane of the gauge fields is introduced.