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Kling, Thomas P.; Aly, Aly

Angular diameter distances reconsidered in the Newman and Penrose formalism. (English) Zbl 1334.83025

Gen. Relativ. Gravitation 48, No. 2, Paper No. 15, 21 p. (2016).
Summary: 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.

MSC:

83C10 Equations of motion in general relativity and gravitational theory
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
83F05 Relativistic cosmology
53Z05 Applications of differential geometry to physics

Keywords:

Dyer-Roeder equation; Newman-Penrose spin coefficient formalism; gravitational lensing; geodesic deviation equation; Friedman-Robertson-Walker (FRW) space-time
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References:

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