The distortion of the area distance-redshift relation in inhomogeneous isotropic universes

We show that areas corresponding to an observed solid angle can be quite different than would be estimated from the corresponding Friedmann-Lemaitre model, even when averaged over large angular scales. This paper concentrates on the specific example of spherically symmetric but spatially inhomogeneous dust universes, the Lemaitre-Tolman-Bondi models, and shows that 'radial lensing' significantly distorts the area distance-redshift and density-redshift relations in these exact solutions compared with the standard ones for Friedmann-Lemaitre models. Thus inhomogeneity may introduce significant errors into distance estimates based on the standard FL relations, even after averaging over large angular scales. Three examples show the area distance versus redshift graph can become multi-valued and form loops, and that the standard FL relations are not recovered even when the distant universe surrounding an inhomogeneity is exactly the background or average FL model. In addition, a useful new gauge choice is presented for these models, solving the problem of locating the past null cone exactly.