  Based on quantum field theory, we formulate the Wigner function and quantum
kinetic theory for polarized photons in curved spacetimes which admit a
covariantly constant timelike vector. From this framework, the photonic
chiral/zilch vortical effects are reproduced in a rigidly rotating coordinate.
In a spatially inhomogeneous coordinate, we derive the spin Hall effect for the
photon helicity current and energy current in equilibrium. Our derivation
reveals that such photonic Hall effect are related to the photonic vortical
effect via the Lorentz invariance and their transport coefficients match each
other.
