= Distance duality relation
{title2=$D_L=(1+z)^2D_A$}
In metric light propagation with <photon> conservation and the usual reciprocity assumptions, <luminosity distance> and <angular diameter distance> satisfy $D_L=(1+z)^2D_A$. Comparing received flux with apparent angular area then gives the bolometric <cosmological surface-brightness dimming> factor $(1+z)^{-4}$. Absorption, <photon> conversion or an inconsistent definition of emitted/observed bands must be treated separately.
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