  We study a gravitating spherically symmetric nonrelativistic configuration
consisting of a spinor fluid whose effective equation of state is derived from
a consideration of a limiting system supported by a massive nonlinear spinor
field. For such a configuration, we find a two-parametric family of static
regular solutions describing compact objects whose masses and sizes are
determined by the central density of the spinor fluid and the mass of the
spinor field. Using the similarity method, we consider a gravitational collapse
of an initially uniform system consisting of the spinor fluid. We estimate the
general characteristics of the collapse and show that a resulting nonuniform
distribution of the fluid occurs that may serve as a core for the creation of
equilibrium starlike configurations.

General Relativity and Quantum Cosmology