# Singularity avoidance for collapsing quantum dust in the Lemaitre-Tolman-Bondi model

## TL;DR

This paper explores quantum effects in collapsing dust clouds, showing that quantum mechanics can prevent classical singularities, leading to a bounce and subsequent expansion instead of a collapse into a singularity.

## Contribution

It introduces a quantum model for dust collapse in the Lemaître-Tolman-Bondi framework that demonstrates singularity avoidance through a bounce mechanism.

## Key findings

- Quantum model prevents classical singularity
- Collapse is replaced by a bounce and expansion
- Constructed a quantum-corrected spacetime for dust collapse

## Abstract

We investigate the fate of the classical singularity in a collapsing dust cloud. For this purpose, we quantize the marginally bound Lemaitre-Tolman-Bondi model for spherically-symmetric dust collapse by considering each dust shell in the cloud individually, taking the outermost shell as a representative. Because the dust naturally provides a preferred notion of time, we can construct a quantum mechanical model for this shell and demand unitary evolution for wave packets. It turns out that the classical singularity can generically be avoided provided the quantization ambiguities fulfill some weak conditions. We demonstrate that the collapse to a singularity is replaced by a bounce followed by an expansion. We finally construct a quantum corrected spacetime describing bouncing dust collapse and calculate the time from collapse to expansion.