  The BPS Skyrme model has been demonstrated already to provide a physically
intriguing and quantitatively reliable description of nuclear matter. Indeed,
the model has both the symmetries and the energy-momentum tensor of a perfect
fluid, and thus represents a field theoretic realization of the "liquid
droplet" model of nuclear matter. In addition, the classical soliton solutions
together with some obvious corrections (spin-isospin quantization, Coulomb
energy, proton-neutron mass difference) provide an accurate modeling of nuclear
binding energies for heavier nuclei. These results lead to the rather natural
proposal to try to describe also neutron stars by the BPS Skyrme model coupled
to gravity. We find that the resulting self-gravitating BPS Skyrmions provide
excellent results as well as some new perspectives for the description of bulk
properties of neutron stars when the parameter values of the model are
extracted from nuclear physics. Specifically, the maximum possible mass of a
neutron star before black-hole formation sets in is a few solar masses, the
precise value depending on the precise values of the model parameters, and the
resulting neutron star radius is of the order of 10 km.
