Hyper-accretion discs around black holes emit copious neutrinos and
anti-neutrinos. A fraction of the emitted neutrinos convert to
electron-positron plasma above the disc through the annihilation reaction
$\nu\bar\nu\to e^+e^-$. This process may drive relativistic jets associated
with GRB explosions. We calculate the efficiency of energy deposition by
neutrinos. Our calculation is fully relativistic and based on a
geodesic-tracing method. We find that the efficiency of neutrino heating is a
well-defined function of (i) accretion rate and (ii) spin of the black hole. It
is practically independent of the details of neutrino transport in the opaque
zone of the disc. The results help identify accretion discs whose neutrino
emission can power GRBs.Comment: 8 pages, 8 figures, accepted for publication in MNRA