The photon gas in the curved space

[micomaco86572]

In a flat space, the momentum of a photon gas distributes isotropically. Every direction is equivalent. If the space is curved,like the space outside a black hole, what will happen to the photon gas? Will the momentum distribution be not isotropic any more?

 

[Dale]

That is correct. Photons going up will lose momentum and photons going down will gain momentum. The net effect is that the photon gas has weight.

 

[micomaco86572]

That is correct. Photons going up will lose momentum and photons going down will gain momentum. The net effect is that the photon gas has weight.

Is there some formula expressing this relationship between metric and the momentum distribution?

 

[Dale]

For a static metric you could use the gravitational time dilation formula and the fact that for massless particles the momentum is proportional to the frequency. For non-static spacetimes I don't know.