Theory of an object with a compact core and its applications

Separate theoretical classifications are proposed for two classes of objects with core-halo structure, loaded polytropes and loaded neutrino objects. The classifications are based on a solution to the relativistic Emden equation which describes the different density distributions and stable equilibrium configurations of both the loaded polytropes and the loaded neutrino objects. The major differences between classical characterizations of compact core objects and the relativistic solution are discussed, and some applications of the theory to the calculation of the redshift distributions of quasars in the Hewitt and Burbridge (1980) catalog are presented