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

## TL;DR

This paper investigates how nested self-similar structures modeled by Lemaitre-Tolman-Bondi metrics affect the propagation of radial light rays, focusing on redshift effects in weak-field regimes.

## Contribution

It introduces a numerical analysis of redshift behavior in self-similar void-overdensity structures within the LTB model, highlighting potential relativistic effects.

## Key findings

- Redshift increases with the number of nested pairs.
- Weak field approximation may still produce significant relativistic effects.
- Nested structures influence light propagation in cosmological models.

## Abstract

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.