  We obtain analogs of the Blandford-Znajek split monopole solution for
force-free magnetospheres around a slowly rotating Kerr-AdS black hole. For
small black holes, we find an analytic solution to first order in the ratio of
horizon radius to AdS scale, $r_H/l$, which exhibits a radial Poynting flux and
for $r_H/l \rightarrow 0$ smoothly approaches the Blandford-Znajek
configuration in an asymptotically flat Kerr background. However, for large
Kerr-AdS black holes with $r_H/l > 1$, namely those for which the bulk black
hole holographically describes the thermodynamics of a strongly-interacting
boundary field theory, the existence of a globally well-defined timelike
Killing vector external to the horizon suggests the absence of energy
extraction through the Blandford-Znajek process. In this regime, we find that
at least for slow rotation the force-free solution still exists but exhibits a
range of angular velocities for the field lines, corresponding to the freedom
in the dual field theory to rotate a magnetic field through a neutral plasma.
As a byproduct of this work, we also obtain an analytic solution for a rotating
monopole magnetosphere in pure AdS, analogous to the Michel solution in flat
space.
