Quantization of Black Holes and Singularity Resolution in Loop Quantum Gravity
Abstract: Loop quantum gravity is based on canonical quantization of holonomy and flux of densitized triads. In loop quantum cosmology (LQC), effective Hamiltonian can be obtained from 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 choice of quantum parameters δ_b,δ_c will lead to different quantization schemes and will result different loop quantum black holes. In this work, 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.