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

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

2002-03-07

arxiv.org/abs/gr-qc/0203026v2

Class.Quant.Grav. 19 (2002) 5877-5901

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1088/0264-9381/19/23/301

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.

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