Abstract
Structure formation within the Lema\^{\i}tre-Tolman model is investigated in a general manner. We seek models such that the initial density perturbation within a homogeneous background has a smaller mass than the structure into which it will develop, and the perturbation then accretes more mass during evolution. This is a generalization of the approach taken by Bonnor in 1956. It is proved that any two spherically symmetric density profiles specified on any two constant time slices can be joined by a Lema\^{\i}tre-Tolman evolution, and exact implicit formulas for the arbitrary functions that determine the resulting LT model are obtained. Examples of the process are investigated numerically.
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