  The interaction of black holes with ambient magnetic fields is important for
a variety of highly energetic astrophysical phenomena. We study this
interaction within the force-free approximation in which a tenuous plasma is
assumed to have zero inertia. Blandford and Znajek (BZ) used this approach to
demonstrate the conversion of some of the black hole's energy into
electromagnetic Poynting flux in stationary and axisymmetric single black hole
systems. We adopt this approach and extend it to examine asymmetric and, most
importantly, dynamical systems by implementing the fully nonlinear field
equations of general relativity coupled to Maxwell's equations. For single
black holes, we study in particular the dependence of the Poynting flux and
show that, even for misalignments between the black hole spin and the direction
of the asymptotic magnetic field, a Poynting flux is generated with a
luminosity dependent on such misalignment. For binary black hole systems, we
show both in the head-on and orbiting cases that the moving black holes
generate a Poynting flux.
