Weak cosmic censorship with SU(2) gauge field and bound on charge-to-mass ratio

We numerically construct the stationary solutions of SU(2) Einstein-Yang-Mills theory in four dimensional anti-de Sitter spacetime. When the t component of the SU(2) gauge field is taken to the only nonzero component, we construct a class of counterexamples to the weak cosmic censorship conjecture in Einstein-Maxwell theory. However, including a nonzero phi component of SU(2) gauge field, we can argue that there is a minimum value qW, when the charge carried by the phi component is larger than this minimum value, for sufficiently large boundary electric amplitude a, the original counterexamples can be removed and cosmic censorship is preserved.