All black holes in Lemaitre-Tolman-Bondi inhomogeneous dust collapse

TL;DR

This paper investigates conditions under which inhomogeneous dust collapse in the Lemaitre-Tolman-Bondi model results in black holes or naked singularities, highlighting the necessity of simultaneous singularity for black hole formation.

Contribution

It identifies specific conditions on density and velocity profiles that determine whether collapse leads to a black hole or a naked singularity in the LTB model.

Findings

Black holes form only with simultaneous singularities in this model.

A unique velocity profile leads to black hole formation for a given density profile.

Most other profiles result in locally naked singularities.

Abstract

Within the Lemaitre-Tolman-Bondi formalism for gravitational collapse of inhomogeneous dust we analyze the parameter space that leads to the formation of a globally covered singularity (i.e. a black hole) when some physically reasonable requirements are imposed (namely positive radially decreasing and quadratic profile for the energy density and avoidance of shell crossing singularities). It turns out that a black hole can occur as the endstate of collapse only if the singularity is simultaneous as in the standard Oppenheimer-Snyder scenario. Given a fixed density profile then there is one velocity profile for the infalling particles that will produce a black hole. All other allowed velocity profiles will terminate the collapse in a locally naked singularity.