Evolution of spherical non-uniform perturbations in the universe

We study the evolution of inhomogeneous spherical perturbations in the universe in a way that generalizes the spherical top-hat collapse in a straightforward manner. For that purpose we will derive a dynamical equation for the density contrast in the context of a Lemaitre-Tolman-Bondi metric and construct solutions with and without a cosmological constant for the evolution of a spherical perturbation with a given initial radial profile. Copyright (C) EPLA, 2010Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq