Shell crossing in generalized Tolman-Bondi spacetimes

TL;DR

This paper investigates shell crossing phenomena in charged dust collapse within generalized Tolman-Bondi spacetimes, revealing that shell crossing is generally inevitable near the center for typical initial conditions.

Contribution

It provides a detailed analysis of shell crossing in charged dust collapse with a cosmological constant, highlighting the dependence on initial data and demonstrating the inevitability of shell crossing in realistic scenarios.

Findings

Shell crossing occurs near the center for generic initial data.

Initial velocity profiles determine shell crossing in non-time-symmetric cases.

Shell crossing typically happens before reaching the minimum bounce radius.

Abstract

We study the occurrence of shell crossing in spherical weakly charged dust collapse in the presence of a non-vanishing cosmological constant. We find that shell crossing always occurs from generic time-symmetric regular initial data, near the center of the matter configuration. For non-time-symmetric initial data, the occurrence---or lack thereof---of shell crossing is determined by the initial velocity profile, for a given mass and charge distribution. Physically reasonable initial data inevitably leads to shell crossing (near the center) before the minimum bounce radius is reached.