  We derive upper and lower limits for the mass-radius ratio of spin-fluid
spheres in Einstein-Cartan theory, with matter satisfying a linear barotropic
equation of state, and in the presence of a cosmological constant. Adopting a
spherically symmetric interior geometry, we obtain the generalized continuity
and Tolman-Oppenheimer-Volkoff equations for a Weyssenhoff spin-fluid in
hydrostatic equilibrium, expressed in terms of the effective mass, density and
pressure, all of which contain additional contributions from the spin. The
generalized Buchdahl inequality, which remains valid at any point in the
interior, is obtained, and general theoretical limits for the maximum and
minimum mass-radius ratios are derived. As an application of our results we
obtain gravitational red shift bounds for compact spin-fluid objects, which may
(in principle) be used for observational tests of Einstein-Cartan theory in an
astrophysical context. We also briefly consider applications of the
torsion-induced minimum mass to the spin-generalized strong gravity model for
baryons/mesons, and show that the existence of quantum spin imposes a lower
bound for spinning particles, which almost exactly reproduces the electron
mass.
