Optical properties of self-similar structure in Lemaitre-Tolman-Bondi model

We explore the effects coming from the nested structures on propagation of radial light rays going through them in the simple self-similar configuration containing pairs of voids and overdense regions. Each pair can be described with the Lemaitre-Tolman-Bondi metric and is composed of interior dust ball and exterior Schwarzschild region. A relation between the redshift and amount of nested pairs is studied numerically in order to answer a question whether a strong relativistic effect can be obtained when every component of the structure can be described by the weak field approximation of general relativity.