  We utilize known exact analytic solutions of perfect fluid hydrodynamics to
analytically calculate the polarization of baryons produced in heavy ion
collisions. Assuming local thermodynamical equilibrium also for spin degrees of
freedom, baryons get a net polarization at their formation (freeze-out). This
polarization depends on the time evolution of the Quark-Gluon Plasma (QGP),
which can be described as an almost perfect fluid. By using exact analytic
solutions, we thus can analyze the necessity of rotation (and vorticity) for
non-zero net polarization. In this paper we give the first analytical
calculations for the polarization four-vector. We use two hydrodynamical
solutions; one is the spherically symmetric Hubble flow (a somewhat
oversimplified model, to demonstrate the methodology). The other solution which
we use is a somewhat more involved one that corresponds to a rotating and
accelerating expansion, and is thus well suited to investigate some main
features of the time evolution of the QGP created in peripheral heavy-ion
collisions (although there are still many numerous features of a real collision
geometry that are beyond the reach of this simple model). Finally we illustrate
and discuss our results on the polarization.
