Perturbed Spherically Symmetric Dust Solution of the Field Equations in Observational Coordinates with Cosmological Data Functions
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In this paper, the Friedmann-Lemaitre-Robertson-Walker spherically symmetric field equations in observational coordinates were formulated and solved using the framework for solving the spheric symmetric Field Equations given by Araujo and Stoeger.Abstract:
Using the framework for solving the spherically symmetric field equations in observational coordinates given by Araujo & Stoeger, we present their formulation and solution in the perturbed Friedmann-Lemaitre-Robertson-Walker spherically symmetric case with observational data representing galaxy redshifts, number counts, and observer area distances as functions of redshift on our past light cone. The importance of the central conditions, those which must hold on our world line , is emphasized. In detailing the solution for these perturbations, we discuss the gauge problem and its resolution in this context as well as how errors and gaps in the data are propagated together with the genuine perturbations. This will provide guidance for solving and interpreting the solutions of the more complicated general perturbation problem with observational data on our past light cone.read more
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