On the relativistic and electrodynamical stability of massive nuclear density cores

TL;DR

This paper develops a unified relativistic model for nuclear density cores, extending classic atomic results to massive cores with up to 10^57 nucleons, revealing stability conditions and electric field properties.

Contribution

It introduces a novel treatment of massive nuclear cores using relativistic Thomas-Fermi equations, generalizing atomic models to astrophysical scales and identifying a new stability island.

Findings

Discovery of a new stability island for A > A_R

Balance of Coulomb repulsion and gravity in massive cores

Presence of overcritical electric fields near the surface

Abstract

We present a unified treatment of nuclear density cores recovering the classic results for neutral atoms with heavy nuclei having a mass number $A\approx 10^2--10^6$ and extrapolating these results to massive nuclear density cores with $A\approx(m_{\rm Planck}/m_n)^3 \sim 10^{57}$. The treatment consists of solving the relativistic Thomas-Fermi equation describing a system of $N_n$ neutrons, $N_p$ protons and $N_e$ electrons in beta decay equilibrium. The $N_p$ protons are distributed at a constant density within a spherical core of radius $R_c$. A new island of stability is found for $A > A_R = 0.039(N_p/A)^{1/2}(m_{Planck}/m_n)^3$. The Coulomb repulsion, screened by relativistic electrons, is balanced by the gravitational self-interaction of the core. In analogy to heavy nuclei they present, near their surface, an overcritical electric field. The relation between $A$ and $N_p$ is generalized to an arbitrary value of the mass number, and the phenomenological relations for $A < 1.5\cdot 10^2$ are obtained as a limiting case.