Energy Extraction From Gravitational Collapse to Static Black Holes

The mass--energy formula of black holes implies that up to 50% of the energy can be extracted from a static black hole. Such a result is reexamined using the recently established analytic formulas for the collapse of a shell and expression for the irreducible mass of a static black hole. It is shown that the efficiency of energy extraction process during the formation of the black hole is linked in an essential way to the gravitational binding energy, the formation of the horizon and the reduction of the kinetic energy of implosion. Here a maximum efficiency of 50% in the extraction of the mass energy is shown to be generally attainable in the collapse of a spherically symmetric shell: surprisingly this result holds as well in the two limiting cases of the Schwarzschild and extreme Reissner-Nordstr\"{o}m space-times. Moreover, the analytic expression recently found for the implosion of a spherical shell onto an already formed black hole leads to a new exact analytic expression for the energy extraction which results in an efficiency strictly less than 100% for any physical implementable process. There appears to be no incompatibility between General Relativity and Thermodynamics at this classical level.Comment: 7 pages, 2 figures, to appear on Int. Journ. Mod. Phys.

On the frequency of oscillations in the pair plasma generated by a strong electric field

We study the frequency of the plasma oscillations of electron-positron pairs created by the vacuum polarization in an uniform electric field with strength E in the range 0.2 Ec < E < 10 Ec. Following the approach adopted in [1] we work out one second order ordinary differential equation for a variable related to the velocity from which we can recover the classical plasma oscillation equation when E -> 0. Thereby, we focus our attention on its evolution in time studying how this oscillation frequency approaches the plasma frequency. The time-scale needed to approach to the plasma frequency and the power spectrum of these oscillations are computed. The characteristic frequency of the power spectrum is determined uniquely from the initial value of the electric field strength. The effects of plasma degeneracy and pair annihilation are discussed.Comment: to appear in Physics Letters

On the structure of the burst and afterglow of Gamma-Ray Bursts I: the radial approximation

We have proposed three paradigms for the theoretical interpretation of gamma-ray bursts (GRBs). (1) The relative space-time transformation (RSTT) paradigm emphasizes how the knowledge of the entire world-line of the source from the moment of gravitational collapse is a necessary condition to interpret GRB data. (2) The interpretation of the burst structure (IBS) paradigm differentiates in all GRBs between an injector phase and a beam-target phase. (3) The GRB-supernova time sequence (GSTS) paradigm introduces the concept of induced supernova explosion in the supernovae-GRB association. These three paradigms are illustrated using our theory based on the vacuum polarization process occurring around an electromagnetic black hole (EMBH theory) and using GRB 991216 as a prototype. We illustrate the five fundamental eras of the EMBH theory: the self acceleration of the $e^+e^-$ pair-electromagnetic plasma (PEM pulse), its interaction with the baryonic remnant of the progenitor star (PEMB pulse). We then study the approach of the PEMB pulse to transparency, the emission of the proper GRB (P-GRB) and its relation to the ``short GRBs''. Finally the three different regimes of the afterglow are described within the fully radiative and radial approximations. The best fit of the theory leads to an unequivocal identification of the ``long GRBs'' as extended emission occurring at the afterglow peak (E-APE). The relative intensities, the time separation and the hardness ratio of the P-GRB and the E-APE are used as distinctive observational test of the EMBH theory and the excellent agreement between our theoretical predictions and the observations are documented. The afterglow power-law indexes in the EMBH theory are compared and contrasted with the ones in the literature, and no beaming process is found for GRB 991216.Comment: 96 pages, 40 figures, to appear on Int. Journ. Mod. Phys.

On the Mass to Charge Ratio of Neutron Cores and Heavy Nuclei

We determine theoretically the relation between the total number of protons $N_{p}$ and the mass number $A$ (the charge to mass ratio) of nuclei and neutron cores with the model recently proposed by Ruffini et al. (2007) and we compare it with other $N_p$ versus $A$ relations: the empirical one, related to the Periodic Table, and the semi-empirical relation, obtained by minimizing the Weizs\"{a}cker mass formula. We find that there is a very good agreement between all the relations for values of $A$ typical of nuclei, with differences of the order of per cent. Our relation and the semi-empirical one are in agreement up to $A\sim 10^4$; for higher values, we find that the two relations differ. We interprete the different behaviour of our theoretical relation as a result of the penetration of electrons (initially confined in an external shell) inside the core, that becomes more and more important by increasing $A$; these effects are not taken into account in the semi-empirical mass-formula.Comment: Some misprints of the published version corrected (value of nuclear density and eq. 7). Talk given at the 4th Italian-Sino Workshop, July 20-30 (2007), Pescara (Italy

The GNSS-R Eddy Experiment II: L-band and Optical Speculometry for Directional Sea-Roughness Retrieval from Low Altitude Aircraft

We report on the retrieval of directional sea-roughness (the full directional mean square slope, including MSS, direction and isotropy) through inversion of Global Navigation Satellite System Reflections (GNSS-R) and SOlar REflectance Speculometry (SORES)data collected during an experimental flight at 1000 m. The emphasis is on the utilization of the entire Delay-Doppler Map (for GNSS-R) or Tilt Azimuth Map (for SORES) in order to infer these directional parameters. Obtained estimations are analyzed and compared to Jason-1 measurements and the ECMWF numerical weather model.Comment: Proceedings from the 2003 Workshop on Oceanography with GNSS Reflections, Barcelona, Spain, 200

Existence and stability for a non-local isoperimetric model of charged liquid drops

We consider a variational problem related to the shape of charged liquid drops at equilibrium. We show that this problem never admits local minimizers with respect to L 1 perturbations preserving the volume. However, we prove that the ball is stable under small C1,1 perturbations when the charge is small enough

An axially-symmetric Newtonian Boson Star

A new solution to the coupled gravitational and scalar field equations for a condensed boson field is found in Newtonian approximation. The solution is axially symmetric, but not spherically symmetric. For N particles the mass of the object is given by $M = Nm - 0.02298 N^3 G_N^2 m^5$, to be compared with $M = Nm - 0.05426 N^3 G_N^2 m^5$ for the spherically symmetric case.Comment: 4 pages, figures available on reques

REIFENBERG FLATNESS FOR ALMOST MINIMIZERS OF THE PERIMETER UNDER MINIMAL ASSUMPTIONS

The aim of this note is to prove that almost minimizers of the perimeter are Reifenberg flat, for a very weak notion of minimality. The main observation is that smallness of the excess at some scale implies smallness of the excess at all smaller scales

Conducting flat drops in a confining potential

We study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external potential. We characterize the semicontinuous envelope of the energy in terms of a parameter measuring the relative strength of the Coulomb interaction. As a consequence, when the potential is confining and the Coulomb repulsion strength is below a critical value, we show existence and partial regularity of volume-constrained minimizers. We also derive the Euler--Lagrange equation satisfied by regular critical points, expressing the first variation of the Coulombic energy in terms of the normal $\frac12$-derivative of the capacitary potential.Comment: 31 page