  Some active galactic nuclei, microquasars, and gamma ray bursts may be
powered by the electromagnetic braking of a rapidly rotating black hole. We
investigate this possibility via axisymmetric numerical simulations of a black
hole surrounded by a magnetized plasma. The plasma is described by the
equations of general relativistic magnetohydrodynamics, and the effects of
radiation are neglected. The evolution is followed for $2000 G M/c^3$, and the
computational domain extends from inside the event horizon to typically $40 G
M/c^2$. We compare our results to two analytic steady state models, including
the force-free magnetosphere of Blandford & Znajek. Along the way we present a
self-contained rederivation of the Blandford-Znajek model in Kerr-Schild
(horizon penetrating) coordinates. We find that (1) low density polar regions
of the numerical models agree well with the Blandford-Znajek model; (2) many of
our models have an outward Poynting flux on the horizon in the Kerr-Schild
frame; (3) none of our models have a net outward energy flux on the horizon;
and (4) one of our models, in which the initial disk has net magnetic flux,
shows a net outward angular momentum flux on the horizon. We conclude with a
discussion of the limitations of our model, astrophysical implications, and
problems to be addressed by future numerical experiments.
