She-Sheng XUE ICRANet, Pescara, Italy How the gravitational energy transfers to the electromagnetic energy for Gamma-Ray-Bursts. 1)Electron-positron production, annihilation, oscillation and thermolization in super-critical electric field. 2) ``Melting’’ phase transition: the nucleon matter core, nuclei matter surroundings. 3) Super-critical electric field on the surface of collapsing core. 4) Electron-positron-photon plasma (dyadosphere) formed in gravitational collapses. 5) Hydrodynamic expansion of Electron-positron-photon plasma. To understand CRITICAL FIELDS IN PHYSICS AND ASTROPHYSICS ``DYADOSPHERE’’

E ~ ergs T ~ 1 sec.

External layers of nuclei matter Super-critical electric field and charge-separation on the surface of massive collapsing core of nucleon matter. Step 1 electrically neutral Melting density Nucleon matter phase Nuclei matter phase Charge separation Supercritical field

Bethe, Borner and Sato, 1971 Fermi-energy (MeV) Density proton Fermi-energy in nuclei matter proton Fermi-energy in nucleon matter ``We see that the slops of the two curves are quite different, indicating a sharp transition... Thus, at the crossing point the nuclei will melt and cease to exist. This melting is completely sharp…within a one-percent of density change.’’

Supercritical field on the surface of massive nuclear cores Degenerate protons and neutrons inside cores are uniform (strong, electroweak and gravitational interactions): Degenerate electrons density -equilibrium electricelectric Electric interaction, equilibrium Poisson equation for Thomas-Fermi system for neutral systems

(in Compton unit) surface Ruffini, Rotondo and Xue (2006,2007,2008) Super Heavy Nuclei Neutron star cores

Black hole Dyadosphere (electron-positron and photon plasma outside the collapsing core) Step-2

Gravitational Collapse of a Charged Stellar Core De la Cruz, Israel (1967); Boulware (1973); Cherubini, Ruffini, Vitagliano (2002) This gives the rate of gravitational collapsing, and we can obtain the rate of opening up phase-space for electrons. Solution: Equation

Pair creation during the gravitational collapse of the massive charged core of an initially neutral star. t R It will be shown that the electric field is magnified by the collapse to E > E c, ….

What happens to pairs, after they are created in electric fields? Polarization currentConduction current f distribution functions of electrons, positrons and photons, S(E) pair production rate and collisions: And Maxwell equations (taking into account back reaction) Vlasov transport equation: Ruffini, Vitagliano and Xue (2004) A naïve expectation !!!

Results of integration (integration time ~ 10 2  C ) Discussions: The electric field strength as well as the pairs oscillate The role of the scatterings is negligible at least in the first phase of the oscillations The energy and the number of photons increase with time Ruffini, Vitagliano and Xue (2004) Ruffini, Vereshchagin and Xue (2007) Electric energy to pair numbers to pair’s kinetic energy

Time and space scale of oscillations The electric field oscillates for a time of the order of rather than simply going down to 0. In the same time the electromagnetic energy is converted into energy of oscillating particles Again we find that the microscopic charges are locked in a very small region: Ruffini, Vitagliano and Xue (2005) compared with gravitational collapse time-space scale Phase-space and Pauli blocking

E r EcEc r+r+ r dya E max A specific Dyadosphere example E dya Electron-positron-photon plasma G. Preparata, R. Ruffini and S.-S. Xue 1998 (Reissner-Nordstrom geometry)

External layers of nuclei matter Black hole Electron-positron-photon plasma expansion, leading to GRBs Step-3

R t Plasma oscillations Already discussed Thermal equilibrium Aksenov, Ruffini Vereshchagin(2007) Core collapsing, plasma formation and expansion Ruffini, Salmonson, Wilson and Xue (1999) Ruffini, Salmonson, Wilson and Xue (2000)

Equations of motion of the plasma The redshift factor  encodes general relativistic effects Ruffini, Vitagliano and Xue (2004) (II) Part of the plasma expanding outwards (I) Part of the plasma falling inwards

The existence of a separatrix is a general relativistic effect: the radius of the gravitational trap is The fraction of energy available in the expanding plasma is about 1/2

Fraschgetti, Ruffini, Vitagliano and Xue (2005) Predictions on luminosity, spectrum and time variability for short GRBs. (1) The cutoff of high-energy spectrum (2) Black-body in low-energy spectrum (3) Peak-energy around ~ MeV

Fraschgetti, Ruffini, Vitagliano and Xue (2006) (4) soft to hard evolution in spectrum (5) time-duration about 0.1 second