Semiclassical Approximation And Low-laying Quasinormal Modes Of Black Holes

The perturbations of black holes have been studied for many years. It is well-known that there are three stages during the evolution of the field perturbation in the black hole background: the initial outburst from the source of perturbation, the quasinormal oscillations and the asymptotic tails. The frequencies and damping time of the quasinormal oscillations called "quasinormal mode" (QNM) are determined only by the black hole's parameters and independent of the initial perturbations. QNM frequencies (QNMs) is one of the important and exciting themes in the black hole physics. A great deal of efforts have been devoted to the black hole's QNMs for the possibility of direct identification of black hole existence through gravitational wave detectors in the near future.The discovery of the AdS/CFT correspondence and the expanding universe motivated the investigation of QNMs in de Sitter and anti-de Sitter space-time in past few years. Attempts to quantize the black hole area also make QNMs more important in fundamental physics.Many methods have been developed in evaluating the QNMs, such as evolving the time dependent wave equation method, integration of the time independent wave equation method, semi-classical method and fraction function method. In this thesis, we adopt semi-classical method include WKB approach and Poshl-Teller approach methods to study the low-laying QNMs.The thesis is organized as follows:In Sec. 1, a brief introduction of black hole's characters, development of black hole physics and the progress of QNMs are given.In Sec. 2, we adopt third order WKB approach and series expansion methods to study the massive scalar fields and Dirac fields QNMs of Schwarchild black holes with global monopole in de Sitter space-time and discuss the influence on QNMs of global monopole, masses of fields and the cosmological constant.In Sec. 3, we adopt the Poshl-Teller approach and series expansion methods...