Quantization of a black-hole gravity: geometrodynamics and the quantum

Abstract

Quantum gravity is effective in domains where both quantum effects and gravity are essential, such as in the vicinity of space-time singularities. This paper will investigate the quantization of a black-hole gravity, particularly the region surrounding the singularity at the origin of the coordinate system. Describing the system with a Hamiltonian formalism, we apply the covariant integral quantization method to find the Wheeler–DeWitt equation of the model. We find that the quantized system has a discrete energy spectrum in the region inside the event horizon. Through the Kantowski–Sachs metric, it is possible to correlate the entropic time, which gives the dynamics for this model, to the cosmic time in a non-trivial way. Different configurations for the phase space of a Schwarzschild black hole are obtained in a semi-classical analysis. For lower-energy states, the quantum corrections result in singularity removal and wormhole formation.