Vacuum polarization in Siklos spacetimes

We study the effect of one-loop vacuum polarization on photon propagation in Siklos spacetimes in the geometric optics limit. We show that for photons with a general polarization in the transverse plane, the quantum correction vanishes in spacetimes with $H_{xy}=0$. For photons polarized along a transverse axis, subluminal and superluminal solutions are admitted for certain subclasses of Siklos spacetimes. We investigate the results in the Kaigorodov and Defrise spacetimes and obtain explicit expressions for the phase velocities. In Kaigorodov spacetime with $H\sim x^3$, photons polarized along the $x$ axis are subluminal in regions where $H$ is positive and superluminal in regions where $H$ is negative, while photons polarized along the $y$ axis are superluminal in $H>0$ regions and subluminal in $H<0$ regions. In the Defrise spacetime, $H\sim x^{-2}$, $x$-polarized and $y$-polarized photons are superluminal for $H<0$, and subluminal for $H>0$. We comment on motion in other Siklos spacetimes.