A new approach for doing theoretical and numeric work with Lemaitre-Tolman-Bondi dust models

Abstract

We introduce quasi-local integral scalar variables for the study of spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models. Besides providing a covariant, and theoretically appealing, interpretation for the parameters of these models, these variables allow us to study their dynamics (in their full generality) by means of fluid flow evolution equations that can be handled with simple numerical techniques and has a significant potential for astrophysical and cosmological applications. These evolution equations can also be understood in the framework of a gauge invariant and covariant formalism of spherical non-linear perturbations on a FLRW background. The covariant time splitting associated with the new variables leads, in a natural way, to rephrase the known analytic solutions within an initial value framework in which covariant scalars are given by simple scaling laws. By using this re-parametrization of the analytic solutions, we re-examine and provide an alternative outlook to various theoretical issues already treated in the literature: regularity conditions, an Omega parameter, as well as the fitting of a given LTB model to radial profiles of density or velocity at different cosmic times. Other theoretical issues and numeric applications will be examined in separate articles.

24 pages, RevTeX two column style, no figures. Typos corrected, references added

References in corpus (9)

• Effect of inhomogeneities on the expansion rate of the Universe
• The effect of inhomogeneous expansion on the supernova observations
• Can inhomogeneties accelerate the cosmic volume expansion?
• Apparent and average acceleration of the Universe
• Accelerated expansion without dark energy
• On average properties of inhomogeneous cosmologies
• On spatial volume averaging in Lema\^ıtre--Tolman--Bondi dust models. Part I: back reaction, spacial curvature and binding energy
• Quasi-local variables and inhomogeneous cosmological sources with spherical symmetry
• On a Quasi-Local Energy Outside the Cosmological Horizon

Cited by in corpus (5)

• Establishing homogeneity of the universe in the shadow of dark energy
• A novel approach to the dynamics of Szekeres dust models
• Back-reaction and effective acceleration in generic LTB dust models
• Radial asymptotics of Lemaitre-Tolman-Bondi dust models
• Geometric and physical properties of closed ever expanding dust models