Spacetime singularities in quantum gravity

Spacetime singularities are a generic feature of the classical theory of general relativity. However, it is in the quantum gravity regime that one could hope to reveal their true nature. The effects of spacetime quantization on singularities can be studies using tools from (2+1)-dimensional quantum gravity. Hosoya's “Quantum Generalized Affine Parameter” (QGAP) is a key tool used in this analysis. Using these tools, I investigate the black hole and the cosmological singularities in (2+1)-dimensional quantum gravity. The spacetime singularity of the BTZ black hole is studied in quantum gravity using generic Gaussian wave functions. It is shown that many paths for classical observers reach the singularity in finite QGAP “time”, suggesting that the singularity is preserved in quantum regime. QGAP is also used to study singularities of the Torus Universe. Using generic Gaussian wave functions and the modular invariant wave functions of the Torus Universe, it is shown that for classical observers many families of paths reach the singularity within finite QGAP, implying that the singularities for this spacetime are also preserved in the quantum regime.