Hawking Radiation As Quantum Tunneling And Canonical Ensemble

The graduate thesis is about the further research of Parikh-Wilczek quantum tunneling for Hawking radiation. It includes two aspects. The one is to proof the universality of Parikh-Wilczek tunneling probabil-ity. We extract some key properties of particle emission from Parikh and Wilczek's original quantum tunneling model and other general-ized researches. These properties are reformulated in terms of modern differential geometry. Then we construct the proof for particle's u-niversal near-horizon behavior. The universal behavior leads to the universality of tunneling rate, which the probability is proportional to the exponential of decrease of horizon's entropy. The other aspect is to try to apply ensemble method to investigate the Parikh-Wilczek tun-neling probability. Since the universality of the relationship between the tunneling rate and the change of horizon's entropy is similar to the probability of the particular micro-state of the thermal system which is given by ensemble. We assume the canonical ensemble with high order is exactly the multi-particles generalization of Parikh-Wilczek's single particle tunneling. The partition function derived by this assumption is used to study the correction of the energy flux of Schwarzschild black hole and the lifespan of black hole. One interesting result is, when the mean-field approximation is applied, the whole system composed by radiation and black hole has different phases which are controlled by the selection of IR cut-off.