Efficiency of Neutrino Annihilation around Spinning Black Holes

A fraction of neutrino emission from GRB accretion disks annihilates above the disk, creating e+- plasma that can drive GRB explosions. We calculate the efficiency of this annihilation using the recent detailed model of hyper-accretion disks around Kerr black holes. Our calculation is fully relativistic and based on a geodesic-tracing method. We find that the efficiency is a well-defined function of (1) accretion rate and (2) spin of the black hole. It is practically independent of the details of neutrino transport in the opaque zone of the disk. The results help identify the accretion disks whose neutrino emission can power GRBs.