She-Sheng XUE ICRANet, Pescara, Italy

1. CRITICAL FIELDS IN PHYSICS AND ASTROPHYSICS OF NEUTRON STARS AND BLACK HOLES Research topics 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. She-Sheng XUE ICRANet, Pescara, Italy To understand how the gravitational energy transfers to the electromagnetic energy for Gamma-Ray-Bursts.

2. International and ICRANet Participants: 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) PhD and MS Students: G. De Barros L. J. Rangel Lemos B. Patricelli J. Rueda M. Rotondo * passed away

3. E ~ 1054 ergs T ~ 1 sec.

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

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

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

7. The “Black hole” energy:E2 = (Mirc2 + Q2/2r)2 + (Lc/r)2 + p2 Christodoulou, Ruffini, 1971

8. + - Sauter, Heisenberg, Euler, 1935, Schwinger, 1951 Damour & Ruffini 1974 • In a Kerr-Newmann black hole vacuum polarization process occurs if3.2MSun£ MBH£ 7.2·106MSun • Maximum energy extractable 1.8·1054 (MBH/MSun) ergs • “…naturally leads to a most simple model for the explanation of the recently discovered g-rays bursts” Electron-positron pairs production and Dyadosphere Heisenberg Damour The Dyadosphere: electron-positron-photon plasma of size ~ 108 cm, temperature ~ 10MeV, and total energy ~ 1051-54 ergs. G. Preparata, R. Ruffini and S.-S. Xue (1998) Ruffini Preparata

9. E Emax Ec r+ rdya r A specific Dyadosphere example Edya Electron-positron-photon plasma (Reissner-Nordstrom geometry) G. Preparata, R. Ruffini and S.-S. Xue 1998

10. (Kerr-Newmann geometry)

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

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

13. Results of numerical integration(integration time ~ 102tC) • 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)

14. Conclusions • The electric field oscillatesfor 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)

15. 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 electric Poisson equation for Thomas-Fermi system for neutral systems

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

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

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

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

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

21. 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

22. 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)

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