Spacetime singularities in (2+1)-dimensional quantum gravity

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 the singularities of the (2 + 1) -dimensional BTZ black hole and the (2 + I)-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 wavefunctions, I show that both the BTZ black hole and the torus universe contain families of paths that still reach the singularities with finite QGAPs, suggesting that singularities persist in quantum gravity. More realistic calculations, using modular-invariant wavefunctions of Carlip and Nelson for the torus universe, further support this conclusion.