Do spikes persist in a quantum treatment of spacetime singularities?

TL;DR

This paper investigates whether quantum effects eliminate classical spikes near spacetime singularities by applying an affine quantization approach to the Hamiltonian system describing the singularity's dynamics.

Contribution

It introduces an affine quantization method to analyze quantum spacetime singularities and demonstrates that quantum effects prevent the formation of classical spikes.

Findings

Quantum spikes do not persist in the affine quantization framework.

Affine quantization provides a suitable formalism for quantum gravitational systems.

Classical sharp features are smoothed out by quantum effects.

Abstract

The classical approach to spacetime singularities leads to a simplified dynamics in which spatial derivatives become unimportant compared to time derivatives, and thus each spatial point essentially becomes uncoupled from its neighbors. This uncoupled dynamics leads to sharp features (called "spikes") as follows: particular spatial points follow an exceptional dynamical path that differs from that of their neighbors, with the consequence that, in the neighborhood of these exceptional points, the spatial profile becomes ever more sharp. Spikes are consequences of the BKL-type oscillatory evolution towards generic singularities of spacetime. Do spikes persist when the spacetime dynamics is treated using quantum mechanics? To address this question, we treat a Hamiltonian system that describes the dynamics of the approach to the singularity and consider how to quantize that system. We argue that this particular system is best treated using an affine quantization approach (rather than the more familiar methods of canonical quantization) and we set up the formalism needed for this treatment. Our investigation, based on this affine approach, shows the nonexistence of quantum spikes.