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Deriving The Dyer-Roeder Equation From The Geodesic Deviation Equation Via The Newman-Penrose Null Tetrad, Aly Aly

Undergraduate Review

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 …