Relativistic effects on neutrino pair annihilation above a Kerr black hole with the accretion disk

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 behavior of the neutrinos 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 a small a, the bending effect becomes dominant and makes the energy increase by factor of 2 compared with that which neglects the relativistic effects. For the disk with a 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 a large a, play a negative role in avoiding the baryon contamination problem in gamma-ray bursts.