Quantization of black holes and singularity resolution in loop quantum gravity.


In this dissertation, we study the properties of quantum black holes in the framework of loop quantum gravity. Loop quantum gravity is based on the canonical quantization of holonomies and fluxes of densitized triads. In loop quantum cosmology (LQC), the effective Hamiltonian can be obtained from the classical Hamiltonian by polymerization. The interior of Schwarzschild black hole is isometric to Kantowski-Sachs cosmological model with symmetry group R × SO(3). Thus loop quantization techniques of LQC can be used in loop quantization of black holes. On the other hand, different choices of quantum parameters δb, δc correspond to different quantization schemes and will lead to different loop quantum black hole solutions. In particular, we investigate global and local properties of Bodendorfer, Mele, and Münch (BMM) model, Alesci, Bahrami and Pranzetti (ABP) model and Böhmer-Vandersloot (BV) model. We find that different choice of parameters will lead to different asymptotic behaviors. Specifically, for appropriate parameters, BMM model has black hole/white hole structure, ABP model has asymptotic de Sitter solution, while in BV model, black hole/white hole horizon never forms due to large quantum effects.