Angular Diameter Distances Reconsidered in the Newman & Penrose Formalism
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.
Kling, T.P. & Aly, A. (2016). Angular Diameter Distances Reconsidered in the Newman & Penrose Formalism. General Relativity and Gravitation, 48(2), 15. doi: 10.1007/s10714-015-2011-4.
Virtual Commons Citation
Kling, Thomas and Aly, Aly (2016). Angular Diameter Distances Reconsidered in the Newman & Penrose Formalism. In Physics Faculty Publications. Paper 21.
Available at: http://vc.bridgew.edu/physics_fac/21