Attempts at vacuum counterexamples to cosmic censorship in AdS

Abstract

We consider vacuum solutions of four dimensional general relativity with $\Lambda < 0$. We numerically construct stationary solutions that asymptotically approach a boundary metric with differential rotation. Smooth solutions only exist up to a critical rotation. We thus argue that increasing the differential rotation by a finite amount will cause the curvature to grow without bound. This holds for both zero and nonzero temperature, and both compact and noncompact boundaries. However, the boundary metric always develops an ergoregion before reaching the critical rotation, which probably means that the energy is unbounded from below for these counterexamples to cosmic censorship.