Evolution of radial profiles in regular Lemaitre-Tolman-Bondi dust models

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We undertake a comprehensive and rigorous analytic study of the evolution of radial profiles of covariant scalars in regular Lemaitre-Tolman-Bondi dust models.

• We consider specifically the phenomenon of "profile inversions" in which an initial clump profile of density, spatial curvature or the expansion scalar, might evolve into a void profile (and vice versa).
• Previous work in the literature on models with density void profiles and/or allowing for density profile inversions is given full generalization, with some erroneous results corrected.
• We prove rigorously that if an evolution without shell crossings is assumed, then only the 'clump to void' inversion can occur in density profiles, and only in hyperbolic models or regions with negative spatial curvature.