Attempts at vacuum counterexamples to cosmic censorship in AdS

TL;DR

This paper explores vacuum solutions in four-dimensional AdS gravity with differential boundary rotation, finding that beyond a critical rotation, solutions develop unbounded curvature and ergoregions, challenging cosmic censorship.

Contribution

It numerically constructs stationary vacuum solutions with differential rotation in AdS and identifies a critical rotation beyond which solutions become singular, providing potential counterexamples to cosmic censorship.

Findings

Smooth solutions exist only up to a critical rotation

Curvature grows without bound beyond critical rotation

Boundary develops an ergoregion before reaching critical rotation

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.