  The one-loop effective action for QED in curved spacetime contains
equivalence principle violating interactions between the electromagnetic field
and the spacetime curvature. These interactions lead to the dependence of
photon velocity on the motion and polarization directions. In this paper we
investigate the gravitational analogue to the electromagnetic birefringence
phenomenon in the static and radiating topological black hole backgrounds,
respectively. For the static topological black hole spacetimes, the velocity
shift of photons is the same as the one in the Reissner-Nordstr\"om black
holes. This reflects that the propagation of vacuum polarized photons is not
sensitive to the asymptotic behavior and topological structure of spacetimes.
For the massless topological black hole and BTZ black hole, the light cone
condition keeps unchanged. In the radiating topological black hole backgrounds,
the light cone condition is changed even for the radially directed photons. The
velocity shifts depend on the topological structures. Due to the null fluid,
the velocity shift of photons does no longer vanish at the apparent horizons as
well as the event horizons. But the ``polarization sum rule'' is still valid.
