She-Sheng XUE ICRANet, Pescara, Italy how the gravitational energy transfers to the electromagnetic energy for Gamma-Ray-Bursts. 1) Electron-positron production, annihilation and oscillation in super-critical electric field. 2) Super-critical electric field on the surface of collapsing core. 3) Electron-positron-photon plasma formed in gravitational collapses. 4) Hydrodynamic expansion of Electron-positron-photon plasma. To understand Research topics CRITICAL FIELDS IN PHYSICS AND ASTROPHYSICS OF NEUTRON STARS AND BLACK HOLES

F. Fraschetti (CEA Saclay, France) H. Kleinert (Free University of Berlin, Germany R. Klippert (ICRANet, Brazile) G. Preparata* (INFN, University of Milan, Italy) V. Popov (ITEP, Moscow, Russia) R. Ruffini (ICRANet, University of Rome, Italy) J. Salmonson (Livemore National Lab., University of California, USA) L. Vitagliano (ICRANet, University of Salerno, Italy) G. Vereshchagin (ICRANet, Minsk, Belarus) J. Wilson* (Livemore National Lab., University of California, USA) S.-S. Xue (ICRANet) International and ICRANet Participants: PhD and MS Students: G. De Barros L. J. Rangel Lemos B. Patricelli J. Rueda M. Rotondo * passed away

E ~ ergs T ~ 1 sec.

External layers of the star Super-critical electric field and charge-separation on the surface of massive collapsing core

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

External layers of the star Black hole Electron-positron-photon plasma expansion, leading to GRBs

The “Black hole” energy: E 2 = (M ir c 2 + Q 2 /2  ) 2 + (Lc/  ) 2 + p 2 Christodoulou, Ruffini, 1971

+- Sauter, Heisenberg, Euler, 1935, Schwinger, 1951 Damour & Ruffini 1974 In a Kerr-Newmann black hole vacuum polarization process occurs if 3.2M Sun  M BH  7.2·10 6 M Sun Maximum energy extractable 1.8·10 54 (M BH /M Sun ) ergs “…naturally leads to a most simple model for the explanation of the recently discovered  -rays bursts” Electron-positron pairs production and Dyadosphere The Dyadosphere: electron-positron-photon plasma of size ~ 10 8 cm, temperature ~ 10MeV, and total energy ~ ergs. G. Preparata, R. Ruffini and S.-S. Xue (1998) Heisenberg Damour Preparata Ruffini

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)

(Kerr-Newmann geometry )

A general formula for the pair-production rate in non-uniform fields (Kleinert, Ruffini and Xue 2007) Confined (Sauter) field Coulomb field and bound states in collisions of laser beams and heavy ions, neutron stars and black holes. Kleinert

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 numerical 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)

Conclusions 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)

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) Popov Super Heavy Nuclei Neutron star cores

Gravitational Collapse of a Charged Stellar Core De la Cruz, Israel (1967) Boulware (1973) Cherubini, Ruffini, Vitagliano (2002)

An Astrophysical Mechanism of Electromagnetic Energy Extraction: Pair creation during the gravitational collapse of the masive charged core of an initially neutral star. t R If the electric field is magnified by the collapse to E > E c, then…

R t Plasma oscillations Already discussed Thermal equilibrium To be discussed An Astrophysical Mechanism of Electromagnetic Energy Extraction Ruffini, Salmonson, Wilson and Xue (1999) Ruffini, Salmonson, Wilson and Xue (2000) Wilson

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