Photonic spin Hall effect from quantum kinetic theory in curved spacetime

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.