  We study the dynamics of spontaneously formed vortices in homogeneous
microcavity-polariton condensates (MPCs). We find that vortices are stable and
appear spontaneously without stirring or rotating MPCs. The dip of the vortex
core contains some background of reservoir polaritons and the visibility of a
vortex is increasing with respect to the pump strength. The vortex radius is
inversely proportional to the square root of the condensate density. Excitation
energies of vortices at high and low pump powers are finite and zero,
respectively. Vortices at low pump powers exhibit the short lifetime.
