  The general solution of hydrostatic equilibrium equations for a two-component
fluid of ions and electrons without a local electroneutrality constraint is
found in the framework of Newtonian gravity theory. In agreement with the
Poincar\'e theorem on analyticity and in the context of Dyson's argument, the
general solution is demonstrated to possess a fixed (essential) singularity in
the gravitational constant $G$ at $ G = 0 $. The regular component of the
general solution can be determined by perturbation theory in $G$ starting from
a locally neutral solution. The non-perturbative component obtained using the
method of Wentzel, Kramers and Brillouin is exponentially small in the inner
layers of the star and grows rapidly in the outward direction. Near the surface
of the star, both components are comparable in magnitude, and their non-linear
interplay determines the properties of an electro- or ionosphere. The stellar
charge varies within the limits of $- 0.1 $ to $150$ C per solar mass. The
properties of electro- and ionospheres are exponentially sensitive to
variations of the fluid densities in the central regions of the star. The
general solutions of two exactly solvable stellar models without a local
electroneutrality constraint are also presented.
