Genericity aspects in gravitational collapse to black holes and naked singularities

TL;DR

This paper explores the conditions under which gravitational collapse leads to black holes or naked singularities, demonstrating that both outcomes are generic in the space of initial data for spherical matter collapse.

Contribution

It shows that both black holes and naked singularities are generic outcomes of gravitational collapse with general Type I matter fields, including small pressure perturbations.

Findings

Both black holes and naked singularities are generic outcomes.

Small pressure perturbations can change collapse endstates.

Collapse outcomes depend on initial data distribution.

Abstract

We investigate here the genericity and stability aspects for naked singularities and black holes that arise as the final states for a complete gravitational collapse of a spherical massive matter cloud. The form of the matter considered is a general Type I matter field, which includes most of the physically reasonable matter fields such as dust, perfect fluids and such other physically interesting forms of matter widely used in gravitation theory. We first study here in some detail the effects of small pressure perturbations in an otherwise pressure-free collapse scenario, and examine how a collapse evolution that was going to the black hole endstate would be modified and go to a naked singularity, once small pressures are introduced in the initial data. This allows us to understand the distribution of black holes and naked singularities in the initial data space. Collapse is examined in terms of the evolutions allowed by Einstein equations, under suitable physical conditions and as evolving from a regular initial data. We then show that both black holes and naked singularities are generic outcomes of a complete collapse, when genericity is defined in a suitable sense in an appropriate space.