Gamma-ray bursts and the runaway instability of thick discs around black holes

In the context of cosmological models for gamma-ray bursts where the energy is extracted from a thick disc orbiting a stellar-mass black hole we discuss the stability of accretion when the specific angular momentum is increasing outwards in the disc. Discs with constant angular momentum are known to lead to a runaway instability, with catastrophic accretion taking place on a dynamical time-scale. We find that even a slight increase of the specific angular momentum outwards has a strong stabilizing effect on the accretion process. We finally comment on the limitations of our results, which are obtained with classical physics and neglecting the disc self-gravity.