Quantum potential in dust collapse with a negative cosmological constant

TL;DR

This paper models quantum effects in dust collapse within an anti-de Sitter space, showing that quantum potentials can induce a bounce, preventing singularities predicted by classical gravity.

Contribution

It introduces a novel quantum potential analysis of dust collapse in AdS space, leading to a bouncing geometry that avoids classical singularities.

Findings

Quantum potential causes a bounce in collapsing dust.

Quantum effects modify the external spacetime solution.

Collapse is avoided, preventing singularity formation.

Abstract

In the functional Schrodinger formalism, we obtain the wave function describing collapsing dust in an anti-de Sitter background, as seen by a co-moving observer, by mapping the resulting variable mass Schrodinger equation to that of the quantum isotonic oscillator. Using this wave function, we perform a causal de Broglie-Bohm analysis, and obtain the corresponding quantum potential. We construct a bouncing geometry via a disformal transformation, incorporating quantum effects. We derive the external solution that matches with this smoothly, and is also quantum corrected. Due to a pressure term originating from the quantum potential, an initially collapsing solution with a negative cosmological constant bounces back after reaching a minimum radius, and thereby avoids the classical singularity predicted by general relativity.