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We report on the third phase of our study of the neutrino-cooledhyperaccreting torus around a black hole that powers the jet in Gamma RayBursts. We focus on the influence of the black hole spin on the properties ofthe torus. The structure of a stationary torus around the Kerr black hole issolved numerically. We take into account the detailed treatment of themicrophysics in the nuclear equation of state that includes the neutrinotrapping effect. We find, that in the case of rapidly rotating black holes, thethermal instability discussed in our previous work is enhanced and develops formuch lower accretion rates. We also find the important role of the energytransfer from the rotating black hole to the torus, via the magnetic coupling.

The role of black hole spin and magnetic field threading the unstable neutrino disk in Gamma Ray Bursts