Quantum gravitational collapse: non-singularity and non-locality

TL;DR

This paper explores quantum effects in gravitational collapse, showing that quantum mechanics prevents singularities at the origin and introduces non-local effects near classical singularities, while not affecting the horizon for infalling observers.

Contribution

It demonstrates that quantum mechanics removes classical singularities in gravitational collapse and reveals non-local phenomena near the origin, expanding understanding of quantum gravity.

Findings

Quantum effects eliminate classical singularity at the origin.

Non-local effects become significant near the classical singularity.

Quantum horizon behavior remains consistent with classical predictions.

Abstract

We investigate gravitational collapse in the context of quantum mechanics. We take primary interest in the behavior of the collapse near the horizon and near the origin (classical singularity) from the point of view of an infalling observer. In the absence of radiation, quantum effects near the horizon do not change the classical conclusions for an infalling observer, meaning the horizon is not an obstacle for him. However, quantum effects are able to remove the classical singularity at the origin, since the wave function is non-singular at the origin. Also, near the classical singularity, some non-local effects become important. In the Schrodinger equation describing behavior near the origin, derivatives of the wave function at one point are related to the value of the wave function at some other distant point.