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

Abstract

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 ϕ component of SU(2) gauge field, we can argue that there is a minimum value qW, when the charge carried by the ϕ 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.