Investigations On Some Properties Of Hawking Radiation And Isolated Horizons

In 1974, Stephen Hawking discovered that black holes emit a black body spectrum, due to quantum effects near the event horizon, which caused a tremen-dous commotion in the scientific world. From then on, Hawking radiation has garnered lots of interest, since Hawking radiation and four Laws of black hole thermodynamics cause deep, unsuspected connections among classical general relativity, quantum physics and statistical mechanics. The stationary black hole is represented by event horizon. However, this representation of black hole pos-sesses some drawbacks. Firstly, to find the event horizon the knowledge of the metric of the entire spacetime is required, in other words, defining black hole by local conditions is more reasonable. Secondly, the event horizons are determined by the exact solutions of Einstein equation (most of which are of high symmetry), while the real black holes are often distorted by the gravitational interaction with the matter and radiation around them. Finally, the systematic development of black hole thermodynamics requires the description involving local information rather than the data describing distant regions. A successful example of locally-defined black hole is the theory of (weakly) isolated horizons first proposed by Ashtekar and developed by many others. So it is important to investigate the properties of this kind of locally-defined black holes.This dissertation is about the properties of Hawking radiation and isolated horizons. The first chapter is the introduction and review. We briefly review the topics of black hole thermodynamic, the methods to calculate Hawking radia-tion, black hole information loss problem, quantization of the area of black holes, and isolated horizons. In Chapter 2, we investigate the massive Dirac particles’ Hawking radiation from a general static Riemann black hole using Damour-Ruffini method. We consider energy conservation and the back reaction of radiated par-ticles to the spacetime, and find that the radiation spectrum is not thermal. We investigate the tunneling of fermions from a general static Riemann black hole by following the method of Refs. [28,29]. By applying the WKB approximation and the Hamilton-Jacobi ansatz to the Dirac equation, we obtain the standard Hawking temperature. Furthermore, Refs. [28,29] only calculated the tunnel- to investigate the tunneling of Dirac particles with arbitrary spin directions and also obtain the expected Hawking temperature. Then, vector particles tunneling from BTZ black hole, four-dimensional Schwarzschild black hole and Vaidya black holes is investigated. By applying the WKB approximation and the appropriate ansatz for the form of the action to the Proca equation, we obtain the tunneling spectrum of vector particles. As a result, the expected Hawking temperature is recovered. Our results provide further evidences for the universality of black hole radiation. In Chapter 3, we revisit the tunneling spectrum of a charged and rotating black hole-by using Parikh and Wilczek’s tunneling method and get the most general result. We use this general spectrum to discuss the informa-tion recovery based on the Refs. [45,46,47,48]. For the tunneling spectrum we obtained, there exit correlations between sequential Hawking radiations, informa-tion can be carried out by such correlations, and the entropy is conserved during the whole radiation process. So we resolve the information loss paradox based on the methods [45,46,47,48] in the most general stationary case. Then we also investigate the properties of tunneling spectrum from a weakly isolated horizon (WIH)--a locally-defined black hole. We find that for this kind of locally-defined black hole there are the same results as the stationary black holes, so we resolve the information loss paradox based on the methods [45,46,47,48] in a general case. In Chapter 4, based on Parikh and Wilczek’s tunneling method, we have quantized the entropy and the area of a weakly isolated horizon and the apparent horizon of a Vaidya black hole, and obtain the quantized entropy and area spec-trum which are the same as Bekenstein’s original results. Our results indicate that the quantization of entropy of the black hole horizon is a generic property of horizon, and is closely related to Hawking temperature. In Chapter 5, we inves-tigate the electrical and thermodynamical properties of Isolated Horizons. Based on Damour’s method [21], we establish the Ohm’s law and Joule’s law of Isolated Horizons, so we generalize the electrical laws of stationary black holes to Isolated Horizons. We investigate the geometry in the vicinity of non-rotating Isolated Horizons, and find that under the first-order approximation of r,(?)/(?)u is a Killing vector and there exists a Hamiltonian conjugate to it, so (?)/(?)u is a physical observer. We calculate the energy as measured at infinity of a particle at rest outside the horizon and construct a reversible Carnot Cycle with an Isolated Horizon as a cold reservoir, which gives a further confirmation of the thermodynamic nature of Isolated Horizons. At last we give a conclusion.