In this paper we examine the geodesic deviation equation using the Newman-Penrose (N-P) formalism for a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) metric (Carroll, S. (2004); Ryden, B. (2003); Newman & Penrose (1962)). We solved the geodesic deviation equation for angular diameter distance, using the relevant N-P components, and the resulting expression was the Dyer-Roeder equation of cosmology (Ryden, B. (2003)) (Schneider et al. (1992)). This leads us to believe that we can apply the N-P formalism to a perturbed FLRW metric and find a solvable equation for angular diameter distance (Kling & Campbell (2008)). The perturbed FLRW metric incorporates clumps of matter into a metric that is on average homogeneous and isotropic. Deriving a solvable equation for angular diameter distance, in a perturbed FLRW metric, could prove useful to astronomers. By including clumps of matter along the line-of-sight into the math, we can calculate distances to light emitting objects that are obstructed by weak gravitational fields. This thesis should serve as a test of both our tetrad and our methodology, by showing that they work in the flat unperturbed metric.
Thomas Kling (Thesis Director)
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Original document was submitted as an Honors Program requirement. Copyright is held by the author.
Aly, Aly. (2014). Deriving the Dyer-Roeder Equation from the Geodesic Deviation Equation via the Newman Penrose Null Tetrad. In BSU Honors Program Theses and Projects. Item 80. Available at: https://vc.bridgew.edu/honors_proj/80
Copyright © 2014 Aly Aly