Understanding the Dyer-Roeder approximation as a consequence of local cancellations of projected shear and expansion rate fluctuations

It is shown with several concrete examples that the Dyer-Roeder approximation valid in spacetimes which fulfill condition fluctuations expansion rate along a light ray locally cancels shear contribution to redshift. This case for standard cosmological scenarios including perturbed FLRW spacetimes, N-body simulations and Swiss-cheese models. With another example it then illustrated possible construct statistically homogeneous effectively isotropic models do not condition. In this case, invalid. Instead, mean redshift-distance relation can be described using based on spatial averages of transparent part spacetime.