Theoretical Study On Quantum Effects Of Black Holes

Some quantum effects of black holes are discussed in this thesis, including Hawking radiation, quasi-normal modes and the quantization of black holes. Hawking radiation and quasi-normal modes are closely related to the detection of gravitational waves. The former provides theoretical bases for the latter, which will provide experimental evidences for the former. In addition, what the black hole quantization is to the establishment of complete quantum gravity, the hydrogen atom quantization is to quantum mechanics. Therefore, the research on the black hole quantum effects has significant theoretical values.This dissertation consists of four chapters. In the first chapter, the geometric properties of classical black holes are introduced, including an infinite red-shift surface and the horizon of black holes, where, the basic features of Penrose diagram are emphasized in detail. In chapter two, we introduce the basic concepts and calculation methods of the main quantum effects of black holes. After these introductions, we study the Hawking radiation of rotating charged Godel black holes in five-dimensional minimal gauged super-gravity in chapter three. By employing the matching technique, we calculate the corresponding absorption probability and analyze the effect of the three parameters of Godel black holes. Furthermore, we derive the necessary condition for the super-radiance to happen. In chapter four, motivated by the recent work about a new physical interpretation of quasi-normal modes, we investigate the quantization of near-extremal Schwarzschild-de Sitter black holes in four-dimensional space-time. Following Kunstatter's method, we get the black hole area spectrum, and find it is consistent with Bekenstein's supposition about the area spectrum of non-extremal black holes.