  Blandford and Znajek discovered a process by which a spinning black hole can
transfer rotational energy to a plasma, offering a mechanism for energy and jet
emissions from quasars. Here we describe a version of this mechanism that
operates with only vacuum electromagnetic fields outside the black hole. The
setting, which is not astrophysically realistic, involves either a cylindrical
black hole or one that lives in 2+1 spacetime dimensions, and the field is
given in simple, closed form for a wide class of metrics. For asymptotically
Anti-de Sitter black holes in 2+1 dimensions the holographic dual of this
mechanism is the transfer of angular momentum and energy, via a resistive
coupling, from a rotating thermal state containing an electric field to an
external charge density rotating more slowly than the thermal state. In
particular, the entropy increase of the thermal state due to Joule heating
matches the Bekenstein-Hawking entropy increase of the black hole.
