Gravitational Quasinormal Modes In The Spherically Symmetric Black Holes Space Times

As it is an intersectional field of general relative theory,quantum mechanics,particle physics,string theory,thermodynamics,astrophysics and statistics,Black hole(BH)physics occupies an extremely significant position in the modern physics.Disturbance of BH space-time is related to some problems such as the parameters estimation and the stability of black hole.It is well known that there are three stages in the evolution of a black hole perturbed by external fields: initial perturbation phase,quasinormal modes(QNMs),late-time tail.The quasinormal modes is called as ‘characteristic sound' of black hole,becacuse it is only related to the basic parameters of black hole,independent of the initial disturbance.The real part of the quasinormal modes frequency represents the actual frequency of the wave oscillation and the imaginary part represents the speed of the wave decay,so,the intrinsic properties of black hole can be analyzed indirectly by the quasinormal modes frequency of the disturbance field in the black hole space-time.Now gravitational waves have been detected,and the first gravitational wave event is caused from binary black hole merge.The process of binary black hole merge can be divided into three stages:inspiral,merger BH's gravitational,ringdown.Therefore,the experimental observation of the QNMs make it to be can distinguish the black hole from other compact stars and make it to be a direct evidence for black hole's existence.This paper is devoted to studying the gravitational QNMs of black hole and the stability.In addition,it was found that the QNMs of anti-de Sitter(Ad S)black holes have direct interpretation in terms of the dual conformal field theory(CFT).This could be considered as a support of the Ad S/ CFT correspondence.It was argued that QNMs possibly reflect the connection between the classical perturbation of a black hole spacetime and some quantum aspects by relating the real part of the QNMs frequencies to the coupling parameter.Therefore,this paper is devoted to studying gravitational perturbation behavior of some special black holes through numerical methods,and trying to find the relationship between quasinormal modes and characteristic parameters of the black hole,also the stability of the black hole.In this thesis,we focus on the QNMs of black hole,and mainly discuss the gravitational quasi-normal modes for black hole in Anti-de Sitter(Ad S)spacetime.The content is mainly composed of the following five parts: The first part is the introduction.The definition about QNMs of black holes is reviewed.Then,the history and the major motivations leading us to research the QNMs of black holes are introduced.Moreover,some methods to calculate the QNMs of black holes are presented.In the second part,we mainly introduce the metric perturbation of black hole and the external field disturbance of black hole.In the third and fourth chapters,we mainly focus on my works.In chapter three,we study the QNMs of odd gravitational perturbation for the2 R black hole in asymptotically Ad S spacetimes.In chapter four,we describe quasinormal modes(QNMs)for gravitational perturbations of Einstein-Gauss-Bonnet black holes(BHs)in higher dimensional spacetimes.The summery of the thesis and pof future research are given in the last part.The specific arrangement of our work is as follows: In chapter 3,we study the gravitational quasi-normal modes(QNMs)for a static2 R black hole(BH)in Anti-de Sitter(Ad S)spacetime,and the main equations of the corresponding odd parity gravitational perturbations are given.The quasinormal modes of 2R black holes is analyzed by means of Horowitz-Hubeny method and finite difference method.We analyze the relationships between QNM frequencies and the parameters,and then we ues this equation to research the eigenvalue of black holes' s quasinormal frequency and stability of spacetime.The results show that except for the case with?=-1(When?=-1,the static2 R Ad S BH returns to a Schwarzschild Ad S black hole),Re(?)and | Im(?)| both increase as| ?|(where2| |=1/BH?R,BHR is the radius of 2R black hole)increases with n0(28)and n1(28).That means in gravitational perturbations the frequency scales are relevant to the radius of the Ad S BH.Since the temperature scale is also related to the radius in the Ad S BH,the frequency scale depends on the temperature.In terms of the Ad S/CFT correspondence,this implies that with smaller radius,the 2R Ad S BH approaches to equilibrium faster.In chapter 4,we describe quasinormal modes(QNMs)for gravitational perturbations of Einstein-Gauss-Bonnet black holes(BHs)in higher dimensional spacetimes,and derive the corresponding main equation of the gravitational perturbation and the effective potential function.The main point of this paper is,to analyze the dynamic evolution of the Einstein-Gauss-Bonnet BH according to the finite difference method in Ad S spacetimes,varying the value of Gauss-Bonnet coupling parameter?,the dimensionality of spacetime n,and the multipole numbers l,and study the stability of black holes.More remarkably,we have found that vector and scalar perturbations have a negative gap which probably does not cause instability but suppresses the quasinormal ringing to be an exponential tail.However,when? increases to some critical value(?=0.45,0.5,0.35respectively),instability of the QNMs occurs in Einstein-Gauss-Bonnet Ad S spacetime.In accordance with the Ad S/CFT correspondence,instability of the QNMs possibly forecasts limits of holographic applicability in Einstein-Gauss-Bonnet Ad S backgrounds.Therefore,in this study the results we obtained not only contribute? for QNMs of Einstein-Gauss-Bonnet Ad S BHs,but also provide useful reference information for research into Ad S/CFT correspondence?In chapter 5,we give a summary and the expection of future research of the thesis.