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 paper should serve as a test of both our tetrad and our methodology, by showing that they work in the flat unperturbed metric.

Note on the Author

Aly Aly is a double major in physics and mathematics graduating the spring 2015. His research project began in 2014 with funding provided by an Adrian Tinsley Program summer research grant and was mentored by Dr. Thomas Kling (Physics).

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