  We present an energy functional for a Thomas-Fermi type two-fluid model of a
self-gravitating non-rotating charged body, with a non-relativistic kinetic
energy. We prove that, under certain conditions on the total number of
positively charged and negatively charged particles, a minimizer exists and
both fluids have compact support. We prove the same result for special
relativistic kinetic energy, assuming further conditions on the total number of
particles. In the non-relativistic kinetic energy case, we further prove the
uniqueness of the minimizer, as well as present results relating the general
shape of the minimizer to the total number of particles.
