Quantum black hole without singularity

TL;DR

This paper presents a quantum model of a collapsing spherical dust shell that avoids singularities, allowing for unitary evolution and a superposition of black and white hole states.

Contribution

It introduces a rigorous quantization of the dust shell, constructing a self-adjoint Hamiltonian that prevents singularity formation in quantum gravity.

Findings

Quantum evolution is unitary and singularity-free.

The shell can re-expand after contraction, avoiding classical black hole singularity.

The quantum state can be interpreted as a superposition of black and white holes.

Abstract

We discuss the quantization of a spherical dust shell in a rigorous manner. Classically, the shell can collapse to form a black hole with a singularity. In the quantum theory, we construct a well-defined self-adjoint extension for the Hamilton operator. As a result, the evolution is unitary and the singularity is avoided. If we represent the shell initially by a narrow wave packet, it will first contract until it reaches the region where classically a black hole would form, but then re-expands to infinity. In a way, the state can be interpreted as a superposition of a black hole with a white hole.