Angular diameter distances reconsidered in the Newman and Penrose formalism
Abstract
Using the Newman and Penrose spin coefficient (NP) formalism, we provide a derivation of the Dyer-Roeder equation for the angular diameter distance in cosmological space-times. We show that the geodesic deviation equation written in NP formalism is precisely the Dyer-Roeder equation for a general Friedman-Robertson-Walker (FRW) space-time, and then we examine the angular diameter distance to redshift relation in the case that a flat FRW metric is perturbed by a gravitational potential. We examine the perturbation in the case that the gravitational potential exhibits the properties of a thin gravitational lens, demonstrating how the weak lensing shear and convergence act as source terms for the perturbed Dyer-Roeder equation.
Keywords
Cite
@article{arxiv.1601.02475,
title = {Angular diameter distances reconsidered in the Newman and Penrose formalism},
author = {Thomas P. Kling and Aly Aly},
journal= {arXiv preprint arXiv:1601.02475},
year = {2016}
}
Comments
21 pages, 6 figures, accepted to GRG