Study Of The Quasinaomal Modes In Black Hole Spacetimes

Quasinormal mode (QNM) of black holes has been an intriguing subject of discussions for the last three decades. It is believed that QNM is a characteristic sound of black holes which could lead to the direct identification of the black hole existence through gravitational wave observations to be realized in the near future. In addition to its potential astrophysical interest, theoretically QNM was believed as a tool to learn more about black hole and was even argued as a testing ground for fundamental physics. It was found that the QNMs of anti-de Sitter (AdS) black holes have direct interpretation in terms of the dual conformal field theory (CFT). This could serve as a support of the AdS/CFT correspondence. Attempts of using QNMs to investigate the dS/CFT correspondence have also been proposed. It was argued that QNMs might reflect the possible connection between the classical vi-brations of a black hole spacetime and various quantum aspects by relating the real part of the QNM frequencies to the Barbero-Immirzi (BI) parameter, which was introduced by hand in order that loop quantum gravity reproduces correctly the black hole entropy. Recently the quasinormal frequencies was used in studing the black hole phase transition. This thesis is devoted to investigating the perturbation around some special black holes through numerical methods, and trying to find the relationship between thermodynamical and dynamical properties of black holes, to distinguish the dark energy in the time-dependant spacetime, and to find the phase transition.The thesis consists of three parts. The first part is the brief introduction of QNM'definition, importance and status, and several numerical methods are given. The second part is about the studying of the perturbations around some special black holes, including the QNM of charged Kaluza-Klein black hole with squashed horizon and its thermodynamical stability, the QNM of charged Kaluza-Klein black hole with squashed horizon in Godel universe, the QNM of black holes absorbing dark energy, and the signature of the black hole phase transition in QNM. The summery of the thesis and expectation of future research are given in the last part.In Section 1, a brief introduction of QNM'definition, importance and status, and several numerical methods mainly used in studying the QNM are given.In Section 2, the massless scalar perturbation in the background of the charged Kaluza-Klein black holes with squashed horizons was studied by continued fraction method. We find that the position of infinite discontinuities of the heat capacities can be reflected in quasinormal spectrum. This shows the possible non-trivial relation between the thermodynamical and dynamical properties of black holes.In Section 3, the QNM of scalar perturbation in the background of 5 dimensional charged Kaluza-Klein black holes with squashed horizons immersed in the Godel universe was studied. Besides the influence due to the compactness of the extra dimension, we disclose the cosmological rotational effect in the wave dynamics. The wave behavior affected by the Goodel parameter provides an interesting insight into the Godel universe.In Section 4, the perturbations of black holes absorbing dark energy was studied. Due to the accretion of dark energy, the black hole mass changes. We observe distinct perturbation behaviors for absorption of different forms of dark energy onto the black holes. This provides the possibility of extracting information whether dark energy lies above or below the cosmological constant boundary w=-1.In Section 5, the perturbation of the scalar field interacting with the Maxwell field in the background of d-dimensional charged AdS black hole and AdS soliton was studied. Different from the single classical field perturbation, which always has the decay mode in the black hole background, we observe the possible growing mode when the perturbation of the scalar field strongly couples to the Maxwell field. The sudden change of the perturbation to growing mode is also observed in the AdS soliton with electric potential. However in the magnetic charged AdS soliton background, we observe the consistent perturbation behavior when the interaction between scalar field and Maxwell field is considered.In Section 6, we give a summary and the expection of future research of the thesis.