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Blandford and Znajek discovered a process by which a spinning black hole cantransfer rotational energy to a plasma, offering a mechanism for energy and jetemissions from quasars. Here we describe a version of this mechanism thatoperates with only vacuum electromagnetic fields outside the black hole. Thesetting, which is not astrophysically realistic, involves either a cylindricalblack hole or one that lives in 2+1 spacetime dimensions, and the field isgiven in simple, closed form for a wide class of metrics. For asymptoticallyAnti-de Sitter black holes in 2+1 dimensions the holographic dual of thismechanism is the transfer of angular momentum and energy, via a resistivecoupling, from a rotating thermal state containing an electric field to anexternal charge density rotating more slowly than the thermal state. Inparticular, the entropy increase of the thermal state due to Joule heatingmatches the Bekenstein-Hawking entropy increase of the black hole.

Blandford-Znajek process in vacuo and its holographic dual