Perturbed Spherically Symmetric Dust Solution of the Field Equations in Observational Coordinates with Cosmological Data Functions

Using the framework for solving the spherically symmetric field equations in observational coordinates given in Araújo & Stoeger (1999), their formulation and solution in the perturbed FLRW spherically symmetric case with observational data representing galaxy redshifts, number counts and observer area distances, both as functions of redshift on our past light cone, are presented. The importance of the central conditions, those which must hold on our world line C, 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