Geometric derivation of the chronometric redshift

Abstract

The chronometric redshift-distance relation z = tan 2(1/2rho), where rho is the distance in radians in the Einstein metric, is derived by an elementary geometric analysis comparable to that in traditional analysis of the expanding universe model. The differential dTt of Einstein time evolution Tt through time t, as applied to the local Minkowski coordinates x, takes the form sec2(1/2t). At the point of observation t = rho, implying that for a sufficiently localized source, observed wave lengths are a factor of sec2(1/2rho) greater than the corresponding emitted wave lengths.