  Using idealized models of the accretion disk we investigate the relativistic
effects on the energy deposition rate via neutrino pair annihilation near the
rotation axis of a Kerr black hole. Neutrinos are emitted from the accretion
disk. The bending of neutrino trajectories and the redshift due to the disk
rotation and gravitation are taken into consideration. The Kerr parameter, $a$,
affects not only neutrinos' behavior but also the inner radius of the accretion
disk. When the deposition energy is mainly contributed by the neutrinos coming
from the central part, the redshift effect becomes dominant as $a$ becomes
large and the energy deposition rate is reduced compared with that neglecting
the relativistic effects. On the other hand, for small $a$ the bending effect
gets dominant and makes energy increase by factor 2 compared with that
neglecting the relativistic effects. For the disk with temperature gradient,
the energy deposition rate for a small inner radius of the accretion disk is
smaller than that estimated by neglecting the relativistic effects. The
relativistic effects, especially for large $a$, play a negative role in
avoiding the baryon contamination problem in gamma-ray bursts.
