How can the distance duality relation be derived in a model-independent way?

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SUMMARY

The distance duality relation, which connects angular diameter distance and luminosity distance, can be derived using transformations of solid angles under velocity transformations. The original discussion references Etherington's 1933 paper, which presents the relation but is noted for its complexity. For those seeking a model-independent derivation, further exploration of literature that simplifies Etherington's concepts is essential. The lack of responses in the forum indicates a gap in accessible resources for this topic.

PREREQUISITES
  • Understanding of angular diameter distance and luminosity distance
  • Familiarity with Etherington's 1933 paper on distance duality
  • Basic knowledge of solid angle transformations
  • Concepts of velocity transformations in cosmology
NEXT STEPS
  • Research simplified explanations of Etherington's distance duality relation
  • Study solid angle transformations in cosmological contexts
  • Explore model-independent approaches to cosmological distance measures
  • Review contemporary papers that reference or build upon Etherington's work
USEFUL FOR

Astronomers, cosmologists, and physics students seeking to understand the distance duality relation and its derivation in a more accessible manner.

aymer
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Hi ,

I need help from someone who has worked out the distance duality relation (between angular diameter distance and the luminosity distance).I am having trouble deriving it and the Etherington paper is a bit too tough for me where it was first discussed (1933). In one of the reviews its written that it comes when you use the transformation of solid angle under velocity transformation..
 
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Its strange that nobody replied to this...I just want a reference as to wherever an attempt was made to derive the relation in a model/background independent way...i tried reading the Etherington paper (he was the first to introduce it I guess) but its a bit too technical for me...
 

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