Quasinormal Modes And Late-time Tails In The Black Hole Spacetimes

Black hole physics plays an important role in the modern physics as it is an intersectionsl field of general relative theory, quantum mechanics, particle physics, string theory, thermodynamics and statistics. However, there exist many open questions to be addressed in the black hole physics, such as the statistical origin of black hole entropy, the information puzzle and stability of black holes, and so on. The full comprehension of these problems will promote the development of the modern physics more rapidly and help us to understand the nature from the further levels. The quasinormal modes and the late-time tails of perturbational fields in the black hole spacetime are related to the identification and stability of the black holes. Moreover, it is also found that they are connected closely with the AdS/CFT correspondence and loop quantum gravity. Therefore, it is of great importance to investigate the quasinormal modes and the late-time tails in the black hole spacetimes.In this thesis, we first investigate the quasinormal modes of some special black holes by using some numerical methods (such as Poshl-Teller approximation, Wentzel-Kramers-Brillouin(WKB) approximation and continue fraction method) and monodromy technique. Then we adopt to Green function method and study the late-time tails of a coupled scalar field in the black hole spacetime with global monopole. Our main works are as follows:(1) Using the third-order WKB approximation, we evaluate the quasinormal modes of scalar field in the black hole spacetime surrounded by quintessence andfind that the quasinormal frequencies depend on the state parameter (i.e. the ratio between pressure and energy density of dark energy) of quintessence. As the absolute value of the state parameter increases, the real part of quasinormal frequencies decreases and the amplitude of the imaginary part increases. This means that the presence of dark energy makes scalar field damp more rapidly. It is also shown that dark energy restrains the oscillation of field in the black hole spacetime.(2) Adopting to the Poshl-Teller potential approximation and the continue fraction method, we investigate Dirac quasinormal modes in the Garfmkle-Horowitz-Strominger dilaton black hole spacetime. We find that as the paramter a of the dilaton field increases, the real parts of quasinormal frequencies increase, the imaginary part first increases and then decreases. When the overtone n is lower andI is larger, the space of the real part depends only on the parameter a and increases with the increase of a, but that of the imaginary part tends to zero. As the overtone n becomes larger, we find the imaginary part in direct proportion to the overtone n.(3) For the acoustic black hole, we study the quasinormal modes coupled scalar field by using the third-order WKB approximation, and find that, for the lower overtone, the real part increases and the imaginary part decreases as the coupled factor f increases. When f is larger, both the real and imaginary parts are almost the linear function of the coupled factor ï¿¡.(4) In order to probe the universal validity of Hod conjecture, we adopt to the monodromy technique and investigate the asympotic quasinormal modes of the coupled scalar fields in the Garfinkle-Horowitz-Strominger, Gibbons-Maeda and acoustic black holes spacetimes and find their frequency formulas of highdamped quasinormal modes are related to the coupled factor ï¿¡. It is shown that the high damped quasinormal frequencies depend not only on the parameters of black hole spacetimes, but also on the coupled strength between the scalar field and the background metric. This means that Hod conjecture is not valid universally.(5) At last, we study the late-time tails of a coupled scalar field in the space-time of black hole with a global monopole. For the Schwarzschild, Reissner-Nordstrom black holes, the decay factor of the late-time tails depends only on the multiple moment / and the mass \x of perturbationaJ field. However, in the spacetime of black hole with a global monopole, we find that the decay factor depends not only on the the multiple moment I and the mass /n, but also on the coupling between the scalar field and the background spacetime. Furthermore, the scalar field decays more rapidly as the coupled factor ï¿¡ increases.