  We present a theoretical study of vortices in arrays of photon condensates.
Even when interactions are negligible, as is the case in current experiments,
pumping and losses can lead to a finite vortex core size. While some properties
of photon condensate vortices, such as their self-acceleration and the
generation of vortex pairs by a moving vortex, resemble those in interacting
polariton condensates far from equilibrium, in several aspects they differ from
previously studied systems: the vortex core size is determined by the balance
between pumping and tunneling, the core appears oblate in the direction of its
motion and new vortex pairs can spontaneously nucleate in the core region.
