Date
12-18-2014
Document Type
Thesis
Abstract
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.
Department
Physics
Thesis Comittee
Thomas Kling (Thesis Director)
Martina Arndt
Matthew Salomone
Copyright and Permissions
Original document was submitted as an Honors Program requirement. Copyright is held by the author.
Recommended Citation
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