Some remarks on the horizon in the dust cloud collapse

TL;DR

This paper investigates the formation of apparent horizons in dust cloud collapse, showing horizons form far from singularities but may be less detectable near singularities where quantum effects matter.

Contribution

It introduces a method using expansion functions to analyze horizon existence in dust collapse, highlighting its limitations near singularities.

Findings

Horizon exists far from the singularity in dust collapse.

The method has limited applicability near the gravitational singularity.

Quantum effects are important near the singularity.

Abstract

We examine the existence of an apparent horizon in the collapse of an isolated dust cloud using expansion functions. Our results indicate that in the region of spacetime far away from the gravitational singularity, the considered system has a horizon, in which case the singularity is covered. Using this method may have limited applicability in the neighbourhood of the gravitational singularity, where quantum effects are expected to be essential.