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.

The Amati relation in the "fireshell" model

(Shortened) CONTEXT: [...] AIMS: Motivated by the relation proposed by Amati and collaborators, we look within the ``fireshell'' model for a relation between the peak energy E_p of the \nu F_\nu total time-integrated spectrum of the afterglow and the total energy of the afterglow E_{aft}, which in our model encompasses and extends the prompt emission. METODS: [...] Within the fireshell model [...] We can then build two sets of ``gedanken'' GRBs varying the total energy of the electron-positron plasma E^{e^\pm}_{tot} and keeping the same baryon loading B of GRB050315. The first set assumes for the effective CBM density the one obtained in the fit of GRB050315. The second set assumes instead a constant CBM density equal to the average value of the GRB050315 prompt phase. RESULTS: For the first set of ``gedanken'' GRBs we find a relation E_p\propto (E_{aft})^a, with a = 0.45 \pm 0.01, whose slope strictly agrees with the Amati one. Such a relation, in the limit B \to 10^{-2}, coincides with the Amati one. Instead, in the second set of ``gedanken'' GRBs no correlation is found. CONCLUSIONS: Our analysis excludes the Proper-GRB (P-GRB) from the prompt emission, extends all the way to the latest afterglow phases and is independent on the assumed cosmological model, since all ``gedanken'' GRBs are at the same redshift. The Amati relation, on the other hand, includes also the P-GRB, focuses on the prompt emission only, and is therefore influenced by the instrumental threshold which fixes the end of the prompt emission, and depends on the assumed cosmology. This may well explain the intrinsic scatter observed in the Amati relation.Comment: 4 pages, 5 figures, to appear on A&A Letter

Relativistic Thomas-Fermi Model at Finite Temperatures

We briefly review the Thomas-Fermi statistical model of atoms in the classical non-relativistic formulation and in the generalised finite-nucleus relativistic formulation. We then discuss the classical generalisation of the model to finite temperatures in the non-relativistic approximation and present a new relativistic model at finite temperatures, investigating how to recover the existing theory in the limit of low temperatures. This work is intended to be a propedeutical study for the evaluation of equilibrium configurations of relativistic ``hot'' white dwarfs.Comment: 8 pages, Latex wsp9.cls. Proceedings Marcel Grossmann IX, Rome (Italy), 2-9 July 2000 (World Scientific

Pair plasma relaxation time scales

By numerically solving the relativistic Boltzmann equations, we compute the time scale for relaxation to thermal equilibrium for an optically thick electron-positron plasma with baryon loading. We focus on the time scales of electromagnetic interactions. The collisional integrals are obtained directly from the corresponding QED matrix elements. Thermalization time scales are computed for a wide range of values of both the total energy density (over 10 orders of magnitude) and of the baryonic loading parameter (over 6 orders of magnitude). This also allows us to study such interesting limiting cases as the almost purely electron-positron plasma or electron-proton plasma as well as intermediate cases. These results appear to be important both for laboratory experiments aimed at generating optically thick pair plasmas as well as for astrophysical models in which electron-positron pair plasmas play a relevant role.Comment: Phys. Rev. E, in pres

System of self-gravitating bosons

Self gravitating boson system equilibrium configuration

On the core-halo distribution of dark matter in galaxies

We investigate the distribution of dark matter in galaxies by solving the equations of equilibrium of a self-gravitating system of massive fermions (`inos') at selected temperatures and degeneracy parameters within general relativity. Our most general solutions show, as a function of the radius, a segregation of three physical regimes: 1) an inner core of almost constant density governed by degenerate quantum statistics; 2) an intermediate region with a sharply decreasing density distribution followed by an extended plateau, implying quantum corrections; 3) an asymptotic, $\rho\propto r^{-2}$ classical Boltzmann regime fulfilling, as an eigenvalue problem, a fixed value of the flat rotation curves. This eigenvalue problem determines, for each value of the central degeneracy parameter, the mass of the ino as well as the radius and mass of the inner quantum core. Consequences of this alternative approach to the central and halo regions of galaxies, ranging from dwarf to big spirals, for SgrA*, as well as for the existing estimates of the ino mass, are outlined.Comment: 8 pages, 5 figures. Accepted for publication by MNRA

GRB970228 and a class of GRBs with an initial spikelike emission

(Shortened) The Swift and HETE-2 discovery of an afterglow associated possibly with short GRBs opened the new problematic of their nature and classification. This has been further enhanced by the GRB060614 observation and by a re-analysis of the BATSE catalog leading to the identification of a new GRB class with "an occasional softer extended emission lasting tenths of seconds after an initial spikelike emission". We plan: a) to fit this new class of "hybrid" sources within our "canonical GRB" scenario, where all GRBs are generated by a "common engine" (i.e. the gravitational collapse to a black hole); b) to propose GRB970228 as the prototype of the such a class. We analyze BeppoSAX data on GRB970228 in the 40-700 keV and 2-26 keV energy bands within the "fireshell" model. We find that GRB970228 is a "canonical GRB", like e.g. GRB050315, with the main peculiarity of a particularly low CircumBurst Medium (CBM) average density n_{cbm}~10^{-3} #/cm^3. We also simulate the light curve corresponding to a rescaled CBM density profile with n_{cbm}=1 #/cm^3. From such a comparison it follows that the total time-integrated luminosity is a faithful indicator of the GRB nature, contrary to the peak luminosity which is merely a function of the CBM density. We call attention on discriminating the short GRBs between the "genuine" and the "fake" ones. The "genuine" ones are intrinsically short, with baryon loading B \la 10^{-5}, as stated in our original classification. The "fake" ones, characterized by an initial spikelike emission followed by an extended emission lasting tenths of seconds, have a baryon loading 10^{-4} \la B \leq 10^{-2}. They are observed as such only due to an underdense CBM consistent with a galactic halo environment which deflates the afterglow intensity.Comment: 4 pages, 4 figures, to appear on A&A Letter

GRB060218 and GRBs associated with Supernovae Ib/c

We plan to fit the complete gamma- and X-ray light curves of the long duration GRB060218, including the prompt emission, in order to clarify the nature of the progenitors and the astrophysical scenario of the class of GRBs associated to SNe Ib/c. The initial total energy of the electron-positron plasma E_{e^\pm}^{tot}=2.32\times 10^{50} erg has a particularly low value similarly to the other GRBs associated with SNe. For the first time we observe a baryon loading B=10^{-2} which coincides with the upper limit for the dynamical stability of the fireshell. The effective CircumBurst Medium (CBM) density shows a radial dependence n_{cbm} \propto r^{-\alpha} with 1.0<\alpha<1.7 and monotonically decreases from 1 to 10^{-6} particles/cm^3. Such a behavior is interpreted as due to a fragmentation in the fireshell. Analogies with the fragmented density and filling factor characterizing Novae are outlined. The fit presented is particularly significant in view of the complete data set available for GRB060218 and of the fact that it fulfills the Amati relation. We fit GRB060218, usually considered as an X-Ray Flash (XRF), as a "canonical GRB" within our theoretical model. The smallest possible black hole, formed by the gravitational collapse of a neutron star in a binary system, is consistent with the especially low energetics of the class of GRBs associated with SNe Ib/c. We give the first evidence for a fragmentation in the fireshell. Such a fragmentation is crucial in explaining both the unusually large T_{90} and the consequently inferred abnormal low value of the CBM effective density.Comment: 4 pages, 3 figures, to appear in A&A Letter

electron-positron-photon plasma around a collapsing star

We describe electron-positron pairs creation around an electrically charged star core collapsing to an electromagnetic black hole (EMBH), as well as pairs annihilation into photons. We use the kinetic Vlasov equation formalism for the pairs and photons and show that a regime of plasma oscillations is established around the core. As a byproduct of our analysis we can provide an estimate for the thermalization time scale.Comment: 8 pages, 4 figures, to appear in the Proceedings of QABP200