Spacetime Singularities in (2+1)-Dimensional Quantum Gravity

TL;DR

This paper studies how quantization affects singularities in (2+1)-dimensional quantum gravity, finding that many singularities remain despite quantum effects, challenging the idea that quantum gravity always resolves them.

Contribution

It demonstrates that in (2+1)-dimensional quantum gravity, certain singularities persist even after quantization, using generic and modular invariant wave functions.

Findings

Some paths reach singularities with finite quantum generalized affine parameter

Quantum effects do not universally smear or resolve singularities

Results support the persistence of singularities in quantum gravity models

Abstract

The effects of spacetime quantization on black hole and big bang/big crunch singularities can be studied using new tools from (2+1)-dimensional quantum gravity. I investigate effects of spacetime quantization on singularities of the (2+1)-dimensional BTZ black hole and the (2+1)-dimensional torus universe. Hosoya has considered the BTZ black hole, and using a ``quantum generalized affine parameter'' (QGAP), has shown that, for some specific paths, quantum effects ``smear'' the singularity. Using generic gaussian wave functions, I show that both BTZ black hole and the torus universe contain families of paths that still reach the singularities with a finite QGAP, suggesting that singularities persist in quantum gravity. More realistic calculations, using modular invariant wave functions of Carlip and Nelson for the torus universe, further support this conclusion.