The dyadosphere of black holes and gamma-ray bursts

The "dyadosphere" has been defined (Ruffini 1998, Preparata et ai. 1998) as the region outside the horizon of a black hole endowed with an electromagnetic field (abbreviated to EMBH for "electromagnetic black hole") where the electromagnetic field exceeds the critical value, predicted by Heisenberg & Euler (1931) for e(+)e(-) pair production. In a very short time (similar to O((h) over bar/mc(2))), a very large number of pairs is created there. We here give limits on the EMBH parameters leading to a Dyadosphere for 10M(circle dot) and 10(5) M-circle dot EMBH's, and give as well the pair densities as functions of the radial coordinate. We here assume that the pairs reach thermodynamic equilibrium with a photon gas and estimate the average energy per pair as a function of the EMBH mass. These data give the initial conditions for the analysis of an enormous pair-electromagnetic-pulse or "P.E.M. pulse" which naturally leads to relativistic expansion. Basic energy requirements for gamma ray bursts (GRB), including GRB971214 recently observed at z = 3.4, can be accounted for by processes occurring in the dyadosphere. In this letter we do not address the problem of forming either the EMBH or the dyadosphere: we establish some inequalities which must be satisfied during their formation process.