  We propose a grated microcavity setup to form trapped polariton condensates
with parity-time ($\mathcal{PT}$) symmetry and study their polarization
dynamics. The pseudo-conservative dynamics of the Stokes vector in proposed
configuration is preserved in the presence of polariton-polariton interaction.
In the case of weak gain-dissipation inbalance, as compared to the linear
polarization splitting, the polarization Stokes spheres are deformed into
ellipsoids. When linear polarization splitting becomes weak, i.e., when
$\mathcal{PT}$-symmetry is broken for noninteracting system, the Stokes spheres
are transformed into hyperboloids, but the dynamics is still described by
closed trajectories, allowing manipulation of the polarization of polariton
condensate by changing polarization splitting without losing its coherency.
