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

TL;DR

This paper constructs stationary solutions in $SU(2)$ Einstein-Yang-Mills theory in anti-de Sitter space, demonstrating conditions under which weak cosmic censorship can be violated or preserved depending on the gauge field configuration.

Contribution

It introduces new solutions in Einstein-Yang-Mills theory that serve as counterexamples to weak cosmic censorship and identifies a charge threshold for preserving censorship.

Findings

Counterexamples to weak cosmic censorship in Einstein-Maxwell theory.

Existence of a minimum charge $q_W$ for cosmic censorship to hold.

Large boundary electric amplitude can restore censorship.

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 $SU(2)$ 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 $q_W$, 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.