Dyadosphere formed in gravitational collapse
  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. 
Remo Ruffini and She-Sheng Xue