Michael Rotondo

The self-consistent general relativistic solution for a system of degenerate neutrons, protons and electrons in β-equilibrium

Abstract We present the self-consistent treatment of the simplest, nontrivial, self-gravitating system of degenerate neutrons, protons and electrons in β -equilibrium within relativistic quantum statistics and the Einstein–Maxwell equations. The impossibility of imposing the condition of local charge neutrality on such systems is proved, consequently overcoming the traditional Tolman–Oppenheimer–Volkoff treatment. We emphasize the crucial role of imposing the constancy of the generalized Fermi energies. A new approach based on the coupled system of the general relativistic Thomas–Fermi–Einstein–Maxwell equations is presented and solved. We obtain an explicit solution fulfilling global and not local charge neutrality by solving a sophisticated eigenvalue problem of the general relativistic Thomas–Fermi equation. The value of the Coulomb potential at the center of the configuration is e V ( 0 ) ≃ m π c 2 and the system is intrinsically stable against Coulomb repulsion in the proton component. This approach is necessary, but not sufficient, when strong interactions are introduced.

ELECTRODYNAMICS FOR NUCLEAR MATTER IN BULK

We present an approach to analyze the electrodynamics of nuclear matter in bulk using the relativistic Thomas–Fermi equation. We generalize to the case of N ≃ (mPlanck/mn)3 nucleons of mass mn an approach well tested in very heavy nuclei (Z ≃ 106). Particular attention is given to implement the condition of charge neutrality globally on the entire configuration, versus the one usually adopted on a microscopic scale. As the limit N ≃ (mPlanck/mn)3 is approached the penetration of electrons inside the core increases and a relatively small tail of electrons persists leading to a significant electron density outside the core. Within a region of 102 electron Compton wavelength near the core, surface electric fields close to the critical value for pair creation by vacuum polarization effect develop. These results can have important consequences on the understanding of physical process in neutron star structures as well as on the initial conditions leading to the process of gravitational collapse to a black hole.

ON GRAVITATIONALLY AND ELECTRODYNAMICALLY BOUND NUCLEAR MATTER CORES OF STELLAR DIMENSIONS

In a unified treatment we extrapolate results for neutral atoms with heavy nuclei to nuclear matter cores of stellar dimensions with mass numbers A ≈ (mPlanck/mn)3 ~ 1057. We give explicit analytic solutions for the relativistic Thomas–Fermi equation of Nn neutrons, Np protons and Ne electrons in beta equilibrium, fulfilling global charge neutrality, with Np = Ne. We give explicit expressions for the physical parameters including the Coulomb and the surface energies and we study as well the stability of such configurations. Analogous to heavy nuclei these macroscopic cores exhibit an overcritical electric field near their surface.

Relativistic Feynman-Metropolis-Teller treatment at finite temperatures

The Feynman-Metropolis-Teller treatment of compressed atoms has been recently generalized to relativistic regimes and applied to the description of static and rotating white dwarfs in general relativity. We present here the extension of this treatment to the case of finite temperatures and construct the corresponding equation of state (EOS) of the system; applicable in a wide regime of densities that includes both white dwarfs and neutron star outer crusts. We construct the mass-radius relation of white dwarfs at finite temperatures obeying this new EOS and apply it to the analysis of ultra low-mass white dwarfs with

The Blackholic energy and the canonical Gamma‐Ray Burst IV: the “long,” “genuine short” and “fake—disguised short” GRBs

M\lesssim 0.2 M_\odot

ON MAGNETIC FIELDS IN ROTATING NUCLEAR MATTER CORES OF STELLAR DIMENSIONS

. In particular, we analyze the case of the white dwarf companion of PSR J1738+0333. The formulation is then extrapolated to compressed nuclear matter cores of stellar dimensions, systems with mass numbers

Neutral nuclear core vs super charged one

A\approx (m_{\rm Planck}/m_n)^3

ON COMPRESSED NUCLEAR MATTER: FROM NUCLEI TO NEUTRON STARS

or mass

The Electrodynamics of the Core and the Crust components in Neutron Stars

M_{\rm core}\approx M_{\odot}

On the electrodynamical properties of nuclear matter in bulk

, where