The origin of the relativistic wind in gamma-ray bursts: MHD flow from a disk orbiting a stellar mass black hole ?

We compute the mass loss rate from a disk orbiting a stellar mass black hole assuming the flow is guided along magnetic field lines attached to the disk. We then estimate the Lorentz factor of the wind at infinity. We find that the Lorentz factor can reach high values only if severe constraints on the field geometry and the conditions of energy injection are satisfied. We discuss our results in the context of different scenarios for gamma-ray bursts. We mention a risk of 'contamination' of the Blandford-Znajek process by wind material emitted from the disk.