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arXiv · 1601.02475

Angular diameter distances reconsidered in the Newman and Penrose formalism

Thomas P. Kling·Aly Aly
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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.

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Thomas P. Kling, Aly Aly. 2016-01-11. Angular diameter distances reconsidered in the Newman and Penrose formalism. https://doi.org/10.1007/s10714-015-2011-4

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