The correspondence between sonic points of ideal photon gas accretion
  and photon spheres
  In an accretion of fluid, its velocity may transit from subsonic to
supersonic. The point at which such transition occurs is called sonic point and
often mathematically special. We consider a steady-state and spherically
symmetric accretion problem of ideal photon gas in general static spherically
symmetric spacetime neglecting back reaction. Our main result is that the EOS
of ideal photon gas leads to correspondence between its sonic point and the
photon sphere of the spacetime in general situations. Despite of the dependence
of the EOS on the dimension of spacetime, this correspondence holds for
spacetimes of arbitrary dimensions.
