Are we observing black hole spins in jetted Gamma-Ray Bursts?

We note that if the GRB phenomenon follows from the collapse of a massive object forming a black hole and a torus accreting into it, the resulting ejecta can be only related to the mass and angular momentum that characterize the black hole. The opening angle of the fireball then corresponds to a black hole spin. If indeed the fireballs opening angles are as small as recent estimates reported in the literature suggest, then GRB would be produced by almost maximally rotating BH. 1 GRB from maximally rotating black holes ? The most popular models for the engine of long GRB attribute the energetics of the prompt emission (E ∼ 10 erg) and of the afterglow, to the energy released by the accretion of a torus onto a rotating Black Hole (BH) (e.g. Woosley 1993, Vietri & Stella 1998, see Meszaros 2002 for a review). Indeed relativistic numerical simulations and analytical calculations support the view that the collapse of a rotating massive star can lead under rather general assumptions to the formation of a black hole and a disc containing about 10 per cent of the mass (Shibata & Shapiro 2002, Shapiro & Shibata 2002). If the event is catastrophic and not repetitive, the accretion of the whole of the torus should leave as a final result a BH with mass M and angular momentum J , depending on the mass and angular momentum of the progenitor star. From general principles (e.g. the no-hair theorem (Misner, Thorne, Wheeler 1973), the ejecta giving raise to the GRB and afterglow events can be only related to these quantities, M and J , that characterize the BH. Within this scenario we then notice that the BH spin is expected to be directly related to the collimation angle θjet of the relativistic fireball responsible for the GRB emission and vice versa estimated values of θjet can be translated