The photon gas in the curved space

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Discussion Overview

The discussion centers on the behavior of a photon gas in curved space, particularly in the context of gravitational effects such as those near a black hole. Participants explore how the curvature of space may affect the isotropy of momentum distribution in the photon gas.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes that in flat space, the momentum of a photon gas is isotropic, but questions how this changes in curved space, specifically outside a black hole.
  • Another participant agrees that photons moving upwards will lose momentum while those moving downwards will gain momentum, suggesting that this results in the photon gas having weight.
  • A third participant reiterates the previous point about momentum changes and asks if there is a formula that relates the metric of the space to the momentum distribution of the photon gas.
  • One participant suggests that for a static metric, the gravitational time dilation formula could be used, noting that momentum is proportional to frequency for massless particles, but expresses uncertainty regarding non-static spacetimes.

Areas of Agreement / Disagreement

There is some agreement on the effects of curvature on the momentum of photons, but the discussion includes uncertainty regarding the formulation of these effects, particularly in non-static spacetimes. Multiple viewpoints on the implications remain present.

Contextual Notes

Participants acknowledge limitations in their understanding, particularly regarding the application of formulas to non-static spacetimes and the dependence on specific metrics.

micomaco86572
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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?
 
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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.
 
DaleSpam said:
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?
 
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.
 

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