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

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.

30 pages, LaTeX, 1 eps figure (problem with eps figure corrected)

References in corpus (3)

• Singularity Theorems and Their Consequences
• Singularity avoidance by collapsing shells in quantum gravity
• Toward a Quantization of Null Dust Collapse

Cited by in corpus (2)

• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• Classical and Quantum Equations of Motion for a BTZ Black String in AdS Space