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CRITICAL FIELDS IN PHYSICS AND ASTROPHYSICS ``DYADOSPHERE’’ 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 How the gravitational energy transfers to the electromagnetic energy for Gamma-Ray-Bursts. She-Sheng XUE ICRANet, Pescara, Italy E ~ 1054 ergs T ~ 1 sec. External layers of nuclei matter Step 1 electrically neutral Melting density c 3 10 g / cm 14 3 Nucleon matter phase Super-critical electric field and charge-separation on the surface of massive collapsing core of nucleon matter. Nuclei matter phase Charge separation Supercritical field Density k 1/ 3 ( fm) 1 proton Fermi-energy in nuclei matter Fermi-energy (MeV) proton Fermi-energy in nucleon matter Bethe, Borner and Sato, 1971 ``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): -equilibrium Degenerate electrons density Electric interaction, equilibrium e l Poisson equation for V (r ) e c tThomas-Fermi system for neutral systems N p Ne n(r ) n p ne V (r ) / m E (r ) / Ec Super Heavy Nuclei N p 10 N p 10 surface x ~ r Rc (in Compton unit) surface 3 55 Neutron star cores Ruffini, Rotondo and Xue (2006,2007,2008) Step-2 Black hole Dyadosphere (electron-positron and photon plasma outside the collapsing core) Gravitational Collapse of a Charged Stellar Core Equation 2 M dR Q M 02 M0 M d 2R 2R 2 2 0 2 M Q Solution: 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. Pair creation during the gravitational collapse of the massive charged core of an initially neutral star. Q ER 2 R Q Emax 2 r t + + + + R0 , t0 + + + + R It will be shown that the electric field is magnified by the collapse to E > Ec , …. What happens to pairs, after they are created in electric fields? E ~ Ec 0 e e ??? E 0, ??? A naïve expectation !!! Vlasov transport equation: t f t , p eE p f t , p S E f distribution functions of electrons, positrons and photons, S(E) pair production rate and collisions: e e And Maxwell equations (taking into account back reaction) t E j p jc Polarization current Conduction current Ruffini, Vitagliano and Xue (2004) Results of integration (integration time ~ 102 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) (i) E Ec (ii ) E Ec 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 103 104 C 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: l 20C compared with gravitational collapse time-space scale Phase-space and Pauli blocking Ruffini, Vitagliano and Xue (2005) A specific Dyadosphere example Edya E Ec E 0 ee Emax Q r2 Example M 20 M Sun Ec Q 0 .1 G M rdya 108 cm 10 27 ergs / cm 3 n 1032 cm 3 T 1/ 4 1/ 4 10 MeV r+ rdya r Q rds N e C Electron-positron-photon plasma (Reissner-Nordstrom geometry) G. Preparata, R. Ruffini and S.-S. Xue 1998 External layers of nuclei matter Step-3 Black hole Electron-positron-photon plasma expansion, leading to GRBs Core collapsing, plasma formation and expansion e e Aksenov, Ruffini Vereshchagin(2007) Thermal equilibrium t R0 , t0 Already discussed Plasma oscillations ee R Ruffini, Salmonson, Wilson and Xue (1999) Ruffini, Salmonson, Wilson and Xue (2000) t0 ,R0 0 1 8 Q R 02 n0 bT03 2 4 E aT0 2 c Equations of motion of the plasma T 0 (conservat ion of energy - momentum) r const The redshift factor a encodes general relativistic effects 2 2 p p r const 2M Q 2 a 1 2 r r nu 0 (conservat ion of entropy) n r2a 1 const (I) Part of the plasma falling inwards na 1 2 r 4 dr 2 2 c a 1 1 dt n0a 0 R0 2 2 2 r p n0a 01 p r 1 R0 0 na 0 R0 4 (II) Part of the plasma expanding outwards Ruffini, Vitagliano and Xue (2004) The existence of a separatrix is a general relativistic effect: the radius of the gravitational trap is 2GM R* 2 c 2 3 Q 1 1 4 GM The fraction of energy available in the expanding plasma is about 1/2 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 (2005) (4) soft to hard evolution in spectrum (5) time-duration about 0.1 second Fraschgetti, Ruffini, Vitagliano and Xue (2006)