  We perform the first general relativistic force-free simulations of neutron
star (NS) magnetospheres in orbit about spinning and non-spinning black holes.
We find promising precursor electromagnetic emission: typical Poynting
luminosities at, e.g., an orbital separation of 6.6 times the NS radius are L ~
6 x 10^{42} erg/s for a 1.4 solar-mass NS with a 10^{13}G polar magnetic field.
The Poynting flux peaks within a broad beam of ~40 degrees in the azimuthal
direction and within ~60 degrees from the orbital plane, establishing a
possible lighthouse effect. Our calculations, though preliminary, preview more
detailed simulations of these systems that we plan to perform in the future.
