The correspondence between sonic points of ideal photon gas accretion and photon spheres

Understand

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.