# The photon gas in the curved space

• micomaco86572
In summary, when in a flat space, the momentum of a photon gas is distributed equally in all directions. However, in a curved space, such as the space outside a black hole, the photon gas will experience a change in momentum distribution. This is due to the gravitational time dilation and the fact that the momentum of massless particles is proportional to their frequency. In non-static spacetimes, the relationship between metric and momentum distribution is currently unknown.
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?

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.

## 1. What is a photon gas?

A photon gas is a theoretical model used in physics to describe a collection of photons, which are particles of light. It is a simplified model that treats photons as particles rather than waves.

## 2. How does a photon gas behave in curved space?

In curved space, a photon gas follows the laws of general relativity, which describes how gravity affects the curvature of space. This means that the behavior of the photon gas will be influenced by the curvature of space, and may exhibit different properties than in flat space.

## 3. Can a photon gas exist in nature?

Yes, a photon gas can exist in nature, particularly in high-energy environments such as stars or the early universe. However, it is a theoretical concept and has not yet been directly observed.

## 4. How is a photon gas different from other gases?

A photon gas is different from other gases because it does not have mass or interact with other particles in the same way. It also follows the laws of quantum mechanics rather than classical mechanics.

## 5. What are the practical applications of studying a photon gas in curved space?

Studying a photon gas in curved space can help us better understand the behavior of light in extreme environments, such as near black holes or during the early stages of the universe. This knowledge can also help us develop new technologies, such as advanced imaging techniques or quantum computing.

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