Rebounce and Black hole formation in a Gravitational Collapse Model with Vanishing Radial Pressure

TL;DR

This paper analyzes a gravitational collapse model with zero radial pressure, showing conditions for black hole formation or dispersal, and identifies a scaling relation near the black hole threshold, highlighting similarities with other critical collapse models.

Contribution

It introduces an analytical study of collapse with vanishing radial pressure, revealing a black hole formation threshold and a mass scaling relation, linking it to numerical critical phenomena.

Findings

Collapse can lead to black hole or dispersal depending on initial parameters.

A scaling relation for black hole mass is derived near the threshold.

Model behavior resembles critical phenomena observed in other collapse models.

Abstract

We examine spherical gravitational collapse of a matter model with vanishing radial pressure and non-zero tangential pressure. It is seen analytically that the collapsing cloud either forms a black hole or disperses depending on values of the initial parameters which are initial density, tangential pressure and velocity profile of the cloud. A threshold of black hole formation is observed near which a scaling relation is obtained for the mass of black hole, assuming initial profiles to be smooth. The similarities in the behaviour of this model at the onset of black hole formation with that of numerical critical behaviour in other collapse models are indicated.