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Angular diameter distances reconsidered in the Newman and Penrose formalism

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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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Acknowledgments

AA thanks the Bridgewater State University Adrian Tinsley Program for Undergraduate Research for a Summer Grant that enabled his participation in this project. Both authors would like to thank and recognize Ezra T. Newman, whose eureka moment prompted a deeper examination of this topic.

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Authors and Affiliations

  1. Department of Physics, Bridgewater State University, Bridgewater, MA, 02325, USA

    Thomas P. Kling & Aly Aly

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  1. Thomas P. Kling
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  2. Aly Aly
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Correspondence to Thomas P. Kling.

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Kling, T.P., Aly, A. Angular diameter distances reconsidered in the Newman and Penrose formalism. Gen Relativ Gravit 48, 15 (2016). https://doi.org/10.1007/s10714-015-2011-4

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