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Scientific Report 2007-2009
Theoretical physics
T9. Massive Nuclear Cores, Neutron Stars and Black Holes
One of the greatest challenges in theoretical physics
is the description of the process of gravitational collapse
leading either to the formation of a neutron star or
to the formation of a Kerr-Newmann black hole [1].
We have reviewed our recent progresses in this field
in Ref. [2]. Based on the Euler-Heisenberg-Schwinger
mechanism for electron-positron pair productions and
Ruffini-Christodoulou mass formula for black holes, we
review the progresses in understanding the pair production
region (Dyado-torus) outside a Kerr-Newmann
black hole. The overcritical and undercritical values of
the electric field are shown in Fig. 1. The optically
thick plasma of electron-positron pairs and photons,
formed in the Dyado-torus, after reaching thermal
equilibrium (see Fig. 2), is bound to undergo an ultrarelativistic
expansion, described by the conservations of
energy-momentum and entropy. This accounts for the
energy source of observed gamma-ray bursts. Using the
relativistic Bolzmann-Vlasov and Maxwell equations to
describe the motion of electron-positron pairs created
by the Euler-Heisenberg-Schwinger mechanism and
their back-reaction on the external electric field, as
well as annihilation to photons, we study the time and
spatial scales of plasma oscillation of electron-positron
pairs and time scale for thermalization with photons.
Comparing these time and spatial scales with the time
and spatial scales determined by gravitational collapse
process, it strongly implies that the Dyado-torus can be
dynamically formed during gravitational collapse.
due to the fact that protons are bound by the strong
interaction, while electrons are free from it. As results,
we find a stable and energetically favorable distribution
of electrons, for which electric field on the surface
of neutron star cores is about the critical value. We
study the energy-states of electrons in the Coulomb
potential and calculate the rate of electron-positron
productions. This reveals the electro-dynamical
properties of the core of neutron stars and massive
stars before they gravitationally collapse to black holes.
Figure 2: The density n of pairs and photons (left plot, with
the total density in bold), their spectra dρ/dε (center plot)
and their temperatures θ = kT/(m e c 2 ) along with chemical
potentials φ = ϕ/(m e c 2 ) (right plot) are shown. ε is the energy
of particle in units of electron rest mass energy m e c 2 .
Two different initial conditions were considered: when only
pairs are present with negligible amount of photons, and the
opposite case (upper and lower figures respectively). In both
cases the pair plasma relaxes to thermal equilibrium configuration
on a timescale t th < 10 −12 s for our parameter range,
i.e. much before it starts to expand on the timescale t < 10 −3
s. We also show by dashed lines (on the upper left panel) the
evolution of pairs and photons concentrations when the inverse
3-body interactions are neglected. Further details are
given in Ref. [3].
References
1. R. Ruffini, in The Kerr spacetime: rotating black holes in
general relativity, Cambridge University Press (2009)
2. C. Cherubini et al., Phys. Rev. D 79, 124002 (2009).
3. A.G. Aksenov et al., Phys. Rev. Lett. 99, 125003 (2007).
4. R. Ruffini et al., Int. J. Mod. Phys. D 16, 1 (2007).
Figure 1: Dyado-torus. Details in Ref. [2].
This field has led to a critical analysis of the electrodynamics
of neutron stars. Using the Thomas-Fermi
model to describe degenerate electrons in the core of
neutrons and protons, which is governed by gravitational,
strong and weak interactions, we study the
electrodynamics of neutron star cores. We find that
the electron-density distribution deviates from the
proton-density distribution at the nuclear density,
Authors
A.G. Aksenov 6 , M.G. Bernardini, C.L. Bianco, D. Bini 6 ,
L. Caito, P. Chardonnet 6 , C. Cherubini 6 , G. De Barros, A.
Geralico, L. Izzo, H. Kleinert 6 , B. Patricelli, L.J. Rangel
Lemos, M. Rotondo, J.A. Rueda Hernandez, R. Ruffini, G.
Vereshchagin, S.-S. Xue
http://www.icra.it/
http://www.icranet.org/
Sapienza Università di Roma 32 Dipartimento di Fisica