Stirring a black hole

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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.