A Tolman-Bondi-Lemaitre Cell-Model for the Universe and Gravitational Collapse

TL;DR

This paper introduces a new piecewise Tolman-Bondi-Lemaitre cell-model for the universe that incorporates local inhomogeneities and their evolution, and examines the gravitational collapse outcomes such as black holes or naked singularities.

Contribution

It generalizes existing cosmological models by including evolving inhomogeneities and analyzes collapse scenarios within this framework.

Findings

Collapse can lead to black holes or naked singularities.

Model incorporates time evolution of inhomogeneities.

Generalizes Friedmann and Swiss-cheese models.

Abstract

A piecewise Tolman-Bondi-Lemaitre (TBL) cell-model for the universe incorporating local collapsing and expanding inhomogeneities is presented here. The cell-model is made up of TBL underdense and overdense spherical regions surrounded by an intermediate region of TBL shells embedded in an expanding universe. The cell-model generalizes the Friedmann as well as Einstein-Straus swiss-cheese models and presents a number of advantages over other models, and in particular the time evolution of the cosmological inhomogeneities is now incorporated within the scheme. Important problem of gravitational collapse of a massive dust cloud, such as a cluster of galaxies or even a massive star, in such a cosmological background is examined. It is shown that the collapsing local inhomogeneities in an expanding universe could result in either a black hole, or a naked singularity, depending on the nature of the set of initial data which consists of the matter distribution and the velocities of the collapsing shells in the cloud at the initial epoch from which the collapse commences.