An Exact Solution with $f^2 = 1$ and $\Lambda \ne 0$ in the LTB model

TL;DR

This paper derives an exact solution in the LTB cosmological model with specific parameters, revealing complex structures and their evolution, and shows how it relates to the FRW model.

Contribution

It provides a new exact solution for the LTB model with $f^2=1$ and $\Lambda eq 0$, detailing its complex structure and connection to FRW cosmology.

Findings

Solution exhibits complex structures like shell stripping, collapse, and accretion.

At large times, the solution simplifies to constant Hubble function and density.

Transformation to FRW model demonstrated.

Abstract

The exact solution in the LTB model with $f^2 = 1$, $\Lambda \ne 0$ is studied. The initial conditions for the metrical function and its derivatives generate the solution with complicated structure including the solutions like "stripping of the shell", "collapce" and "core", or "accretion". In the limit of big time the solution allows the constant Hubble function and the density, depending on time. The transformation to the FRW model is shown. Three pictures are available by e-mail.