  We first recall the concept of Dyadosphere (electron-positron-photon plasma
around a formed black holes) and its motivation, and recall on (i) the Dirac
process: annihilation of electron-positron pairs to photons; (ii) the
Breit-Wheeler process: production of electron-positron pairs by photons with
the energy larger than electron-positron mass threshold; the
Sauter-Euler-Heisenberg effective Lagrangian and rate for the process of
electron-positron production in a constant electric field. We present a general
formula for the pair-production rate in the semi-classical treatment of quantum
mechanical tunneling. We also present in the Quantum Electro-Dynamics
framework, the calculations of the Schwinger rate and effective Lagrangian for
constant electromagnetic fields. We give a review on the electron-positron
plasma oscillation in constant electric fields, and its interaction with
photons leading to energy and number equipartition of photons, electrons and
positrons. The possibility of creating an overcritical field in astrophysical
condition is pointed out. We present the discussions and calculations on (i)
energy extraction from gravitational collapse; (ii) the formation of
Dyadosphere in gravitational collapsing process, and (iii) its hydrodynamical
expansion in Reissner Nordstr\"om geometry. We calculate the spectrum and flux
of photon radiation at the point of transparency, and make predictions for
short Gamma-Ray Bursts.
