Effects of Constant Curvature on Radiation: Red-Shift or Unaffected?

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The discussion centers on the effects of constant curvature in space-time on radiation, specifically addressing whether such curvature leads to red-shift or blue-shift phenomena. Participants reference the Friedmann–Lemaître–Robertson–Walker (FRW) metric as a foundational cosmological solution that often exhibits constant spatial curvature. The conversation emphasizes the need for clarity on the type of curvature being analyzed and its implications on radiation behavior. Overall, the consensus indicates that while spatial curvature may remain constant, the curvature scalar can vary over time, influencing radiation dynamics.

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  • Knowledge of general relativity principles
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thehangedman
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If a certain space-time region has a constant curvature (caused by, say, an even distribution of energy over the region) how would radiation be effected by the curvature? Would it create a red-shift / blue-shift as the radiation moved through the region or would it be un-effected?

Has anyone explicitly solved for the metric tensor in the case of an even distribution of energy over a region of space?
 
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Most cosmological solutions are like this. See for example the Wikipedia page "Friedmann–Lemaître–Robertson–Walker metric". ("FRW" works too.)
 
"Curvature" is a rather general term. Do you know what particular sort of curvature you want to be constant, hangedman, or are you just trying to get a "feel" for what curvature is?

I think most of the cosmological solutions will have a constant spatial curvature, for instance, but a time-varying curvature scalar R.
 

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