  A general approach to analyze the electrodynamics of nuclear matter in bulk
is presented using the relativistic Thomas-Fermi equation generalizing to the
case of $N \simeq (m_{\rm Planck}/m_n)^3$ nucleons of mass $m_n$ the approach
well tested in very heavy nuclei ($Z \simeq 10^6$). 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 $N \simeq (m_{\rm Planck}/m_n)^3$ 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 $10^2$ 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 stars structures as well as on the
initial conditions leading to the process of gravitational collapse to a black
hole.
