On the relativistic and electrodynamical stability of massive nuclear density cores

Details On the relativistic and electrodynamical stability of massive nuclear density cores On the relativistic and electrodynamical stability of massive nuclear density cores

2009-03-22

arxiv.org/abs/0903.3727v1

Astronomy and Astrophysics

Astrophysics

Solar and Stellar Astrophysics

5 pages, 3 figures

Scientific paper

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.

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