Quantum healing of classical singularities in power-law spacetimes

TL;DR

This paper investigates a class of power-law spacetimes to determine which classical singularities are resolved in quantum mechanics, showing that many classically singular spacetimes are quantum mechanically nonsingular due to self-adjointness of the Hamiltonian.

Contribution

It identifies conditions under which classical singularities are healed quantum mechanically in power-law spacetimes, expanding understanding of quantum regularization of singularities.

Findings

Many power-law spacetimes are quantum mechanically nonsingular.

Quantum singularities can be excluded by energy conditions.

The work impacts the understanding of cosmic censorship hypotheses.

Abstract

We study a broad class of spacetimes whose metric coefficients reduce to powers of a radius r in the limit of small r. Among these four-parameter "power-law" metrics we identify those parameters for which the spacetimes have classical singularities as r approaches 0. We show that a large set of such classically singular spacetimes is nevertheless nonsingular quantum mechanically, in that the Hamiltonian operator is essentially self-adjoint, so that the evolution of quantum wave packets lacks the ambiguity associated with scattering off singularities. Using these metrics, the broadest class yet studied to compare classical with quantum singularities, we explore the physical reasons why some that are singular classically are "healed" quantum mechanically, while others are not. We show that most (but not all) of the remaining quantum-mechanically singular spacetimes can be excluded if either the weak energy condition or the dominant energy condition is invoked, and we briefly discuss the effect of this work on the strong cosmic censorship hypothesis.