Stirring a black hole

TL;DR

This paper constructs novel asymptotically AdS4 solutions with boundary differential rotation, revealing black hole and horizonless geometries with ergoregions and hair, and discusses phase diagrams and superradiant bounds.

Contribution

It introduces new AdS4 solutions with boundary-induced rotation, analyzing their phase structure, ergoregions, and superradiant bounds from a first principles CFT perspective.

Findings

Existence of horizonless and black hole solutions with boundary rotation.

Development of ergoregions and hair at critical amplitudes.

Derivation of superradiant bound from CFT data.

Abstract

We present novel asymptotically global AdS$_4$ solutions, constructed by turning on a dipolar differential rotation at the conformal boundary. At fixed energy and boundary profile, we find two different geometries: a horizonless spacetime, and a deformed, hourglass shaped black hole with zero net angular momentum. Both solutions exist up to some maximum amplitudes of the boundary profile, and develop an ergoregion attached to the boundary before the maximum amplitude is reached. We show that both spacetimes develop hair as soon as the ergoregion develops. Furthermore, we discuss the full phase diagram, including the possibility of phases with disconnected horizons, by considering the Mathisson-Papapetrou equations for a spinning test particle. Finally, we provide a first principle derivation of the superradiant bound purely from CFT data, and outline possible scenarios for the late time evolution of the system.