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

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

E ~ 1054 ergs T ~ 1 sec. E ~ 1054 ergs T ~ 1 sec.

External layers of the star Super-critical electric field and charge-separation on the surface of 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) 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 External layers of the star Black hole Electron-positron-photon plasma expansion, leading to GRBs

The “Black hole” energy: E 2 = (Mirc 2 + Q 2/2 r)2 + The “Black hole” energy: E 2 = (Mirc 2 + Q 2/2 r)2 + (Lc/r)2 + p 2 Christodoulou, Ruffini, 1971

Electron-positron pairs production and Dyadosphere + Sauter, Heisenberg, Euler, 1935, Schwinger, 1951 Heisenberg Damour Electron-positron pairs production and Dyadosphere + Sauter, Heisenberg, Euler, 1935, Schwinger, 1951 Heisenberg Damour & Ruffini 1974 • • • In a Kerr-Newmann black hole vacuum polarization process occurs if 3. 2 MSun £ MBH £ 7. 2· 106 MSun 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” Damour The Dyadosphere: electron-positron-photon plasma of size ~ 108 cm, temperature ~ 10 Me. V, and total energy ~ 1051 -54 ergs. G. Preparata, R. Ruffini and S. -S. Xue (1998) Preparata Ruffini

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

(Kerr-Newmann geometry) (Kerr-Newmann geometry)

A general formula for the pair-production rate in non-uniform fields in collisions of laser 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

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

Results of numerical integration (integration time ~ 102 t. C) Discussions: • The electric Results of numerical integration (integration time ~ 102 t. 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 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 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 e c Thomas-Fermi system for neutral systems t

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

Gravitational Collapse of a Charged Stellar Core De la Cruz, Israel (1967) Boulware (1973) 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 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 > Ec , then…

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

Equations of motion of the plasma The redshift factor a encodes general relativistic effects Equations of motion of the plasma The redshift factor a encodes general relativistic effects (I) Part of the plasma falling inwards (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 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

Predictions on luminosity, spectrum and time variability for short GRBs. (1) The cutoff of 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 ~ Me. V Fraschgetti, Ruffini, Vitagliano and Xue (2005)

(4) soft to hard evolution in spectrum (5) time-duration about 0. 1 second Fraschgetti, (4) soft to hard evolution in spectrum (5) time-duration about 0. 1 second Fraschgetti, Ruffini, Vitagliano and Xue (2006)