  The "dyadosphere" (from the Greek word "duas-duados" for pairs) is here
defined 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 and Euler for electron-positron pair production. In a very short
time, a very large number of pairs is created there. I give limits on the EMBH
parameters leading to a Dyadosphere for 10 solar mass and 100000 solar mass
EMBH's, and give as well the pair densities as functions of the radial
coordinate. These data give the initial conditions for the analysis of an
enormous pair-electromagnetic-pulse or "PEM-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.
