Gravitational Collapse and Cosmological Constant

TL;DR

This paper investigates how a positive cosmological constant influences the end states of spherical dust collapse, revealing conditions for bounces, black holes, or naked singularities, and how it can obscure certain singularities.

Contribution

It provides a detailed analysis of initial data conditions leading to bounces or singularities in dust collapse with a positive cosmological constant.

Findings

A positive cosmological constant can induce bounces in collapsing dust clouds.

The initial density and velocity profiles determine whether collapse results in a black hole, naked singularity, or bounce.

A positive cosmological term can hide parts of the singularity spectrum present in dust collapse models.

Abstract

We consider here the effects of a non-vanishing cosmological term on the final fate of a spherical inhomogeneous collapsing dust cloud. It is shown that depending on the nature of the initial data from which the collapse evolves, and for a positive value of the cosmological constant, we can have a globally regular evolution where a bounce develops within the cloud. We characterize precisely the initial data causing such a bounce in terms of the initial density and velocity profiles for the collapsing cloud. In the cases otherwise, the result of collapse is either formation of a black hole or a naked singularity resulting as the end state of collapse. We also show here that a positive cosmological term can cover a part of the singularity spectrum which is visible in the corresponding dust collapse models for the same initial data.