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

Abstract

Using the framework for solving the spherically symmetric field equations in observational coordinates given in Araujo and Stoeger (1999), their formulation and solution in the perturbed FLRW sperically 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 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.

Latex 23 pages, no figures, submitted to Astrophysical Journal

References in corpus (1)

• The Limits on Cosmological Anisotropies and Inhomogeneities from COBE Data

Cited by in corpus (10)

• Obtaining the spacetime metric from cosmological observations
• The Mass of the Cosmos
• Determining the metric of the Cosmos: stability, accuracy, and consistency
• The Lemaitre Model and the Generalisation of the Cosmic Mass
• Solving the Observer Metric
• Calculating Observables in Inhomogeneous Cosmologies I: General Framework
• Solving Einstein Field Equations in Observational Coordinates with Cosmological Data Functions: Spherically Symmetric Universes with Cosmological Constant
• Obtaining the Time Evolution for Spherically Symmetric Lemaître-Tolman-Bondi Models Given Data on Our Past Light Cone
• On perfect fluid models in non-comoving observational spherical coordinates
• Finding a Spherically Symmetric Cosmology from Observations in Observational Coordinates -- Advantages and Challenges