Role of initial data in spherical collapse

TL;DR

This paper investigates how initial density, pressure, and velocity profiles in spherical gravitational collapse influence whether the final outcome is a black hole or a naked singularity, emphasizing the importance of initial conditions.

Contribution

It demonstrates that initial data uniquely determines the end state of spherical collapse, providing insights into the conditions leading to black holes or naked singularities.

Findings

Initial data influences collapse outcomes.

Choice of free functions affects end state.

Black hole or naked singularity depends on initial profiles.

Abstract

We bring out here the role of initial data in causing the black hole and naked singularity phases as the final end state of a continual gravitational collapse. The collapse of a type I general matter field is considered, which includes most of the known physical forms of matter. It is shown that given the distribution of the density and pressure profiles at the initial surface from which the collapse evolves, there is a freedom in choosing rest of the free functions, such as the velocities of the collapsing shells, so that the end state could be either a black hole or a naked singularity depending on this choice. It is thus seen that it is the initial data that determines the end state of spherical collapse in terms of these outcomes, and we get a good picture of how these phases come about.