Quasinormal Modes In The Spherically-symmetric Black Hole Spacetimes

Quasinormal modes of black holes have been one of the main topics of relativistic astrophysics for the last few decades. Due to the waves emitted by perturbed black holes there are no normal mode oscillations but instead of quasi-normal mode (QNM) frequencies, with the real part representing the actual frequency of the oscillation and the imaginary part representing the damping. Indeed, quasinormal ringing could provide the direct evidence of the existence of black holes if observed by LIGO (the Laser Interferometric Gravitational Wave Observatory).In this thesis, firstly, the history about quasinormal modes of black holes are reviewed. Then, the major motivations leading us to study the QNMs of black holes are introduced. Moreover, some methods to calculate the QNMs of black hole are presented.Using the third order WKB(Wentzel-Kramers-Brillouin) approximation, the QNMs frequencies of (1+3) stringy black hole for electromagnetic perturbation are obtained. The results show that the parameters that result from the compactification of higher dimensions can influence the quasinormal complex frequencies. That is to say, the results of the quasinormal frequencies contain the information of the parameters of a stringy black hole. Moreover, using the finite difference method, the object picture of the quasinormal ringing of electromagnetic perturbation in (1+3) stringy black hole spacetime has been obtained.At last, the QNMs of Schwarzschild black hole surrounded by quintessence for gravitational perturbation, electro-magnetic perturbation and Dirac perturbation are obtained by the third WKB method. Compared with the situation without quintessence, the results show that, due to the presence of quintessence, gravitational field, Maxwell field and Dirac field damp more slowly.