The Study Of Entropy And Quasinormal Modes Of Black Hole Spacetimes

The black hole entropy and the quasinormal modes of black holes have long been the important and exciting themes in the black hole physics. The statistical explanation of the black hole entropy is one of the most important aspects, and has long been a puzzled problem to many theoretical physicists, therefore, the investigation on this topic will play an improving role in the black hole physics and even quantum gravitation theory. While, it is well known that the complex frequencies of quasinormal modes are independent of the initial perturbation and just decided by parameters of black hole themselves. In a sense, the quasinormal modes can be regarded as a characteristics sound of black holes. It is widely believed direct way to identify the existence of a black hole, when gravitational wave will be detected in the near future.The thesis consists of five parts, and is organized as follows:In Sec.1, a brief introduction of black hole's thermodynamic characters are given at first. Then, the definition, calculation method and motivations of study of the black hole entropy and quasinormal modes are introduced, respectively.In Sec.2. firstly, the entropy of the charged dilaton-axion black hole is calculated for both asymptotically flat and non-flat cases, using the thin-film model. The thin-film model designates that the black hole entropy is contributed of quantum field by a thin film near the black hole horizon, and the results obtained confirm the Bekenstein-Hawking area-entropy formula. The thin-film model method avoids some drawbacks in the original brick-wall method, but the arbitrary cutoff to remove the divergence near the horizon cannot be avoided yet. For this, the entropy of black holes are corrected to leading order in the Planck length, with the newly modified equation of states density motivated by the generalized uncertainty principle, in the regime of the thin-film model method, which drastically solves the ultraviolet divergences of the just vicinity near the horizon replacing the conventional brick-wall method cutoff with the minimal length. Then, the integral equation of entropy can be solved with residue theorem, which is proportional to the black hole horizon area.In Sec.3, adopting three-order WKB approximation method, the quasinormal modes of a black hole with a global monopole surrounded by static spherically-symmetric quintessence matter are calculated, for massive scalar fields and massless Dirac fields perturbation, re-spectively, and the influence of different parameters on quasinormal modes frequency are discussed.In Sec.4, in the deformed Horava-Lifshitz gravity, the black hole quasinormal modes of the massless Dirac field perturbation are calculated, and then the influence of Horava-Lifshitz parameter on quasinormal modes frequency are discussed.A conclusion is presented in the last section.