Instability Of Scalar Fields In High-dimensional RNdS Black Holes And Asymptotic Dilaton AdS Black Holes

The stability of a given configuration is a very important research topic in physics.The understanding of the underlying mechanism for such an instability can help us better understand the dynamics of the system,and predict which system can also show the similar instability.In studying the formation,evolution,and fate of black holes,the study of black hole stability plays a very important role.At the same time,it also has a close relationship with the cosmic censorship conjecture.The purpose of this paper is to study the instability of a scalar field in high-dimensional RNdS black hole and its relationship with cosmic censorship conjecture by calculating its quasi-normal mode on the black hole background space-time.In addition,we also study the superradiation phenomenon of Dilaton AdS black hole and the corresponding instability.In Chapter 1,not only do we provide a brief review of the basic knowledge of black holes and the relevant history of black hole research,but also we present some exact solutions of Einstein's field equations as well as the relevant concepts.In particular,we introduce the concept of black hole instability with the stability of Schwarzschild black hole and some other black holes in higher dimensions explained briefly.In addition,we also present the WKB approximation and numerical method for the computation of the quasi-normal mode.In Chapter 2,we apply the WKB approximation method to calculate the quasinormal mode of a charged scalar field on top of the high-dimensional RNdS black holes.Starting from the field equation of the scalar field,using the WKB approximation method to analyze the characteristic resonance frequency of the system,we obtain the algebraic equations for the real and imaginary parts of the quasi-normal mode are based on the quantization conditions.In addition,under the condition that the dimensionless electrical coupling constant is arbitrarily small,we obtain an analytic expression for the quasinormal mode of the near extremal charged RNdS black hole.As a result,the highdimensional RNdS black hole is found to be unstable,which nevertheless has nothing to do with the superradiance phenomenon of RNdS black hole.The potential relationship between the instability and the cosmic censorship conjecture is also discussed.In Chapter 3,we have conducted a detailed study on the superradiation effect of the charged scalar field in the asymptotically Dilatonic AdS black hole and its dynamic time-domain evolution process.The instability of the system,triggered by the Dirichlet boundary condition at infinity in AdS space,is called the charged superradiation effect of the scalar field.To calculate the quasinormal mode of the scalar field in a black hole,we adopt two approaches.One is the time domain analysis,and the other is the frequency domain analysis.To simplify the calculation,we work with the Eddington-Finkelstein coordinates.In the time domain analysis,the dynamic time evolution behavior of the scalar field is studied,leading to the exponential growth behavior of the scalar field amplitude over time.In the frequency domain analysis,the quasi-normal mode of the scalar field is calculated,where the superrradiance unstable frequency mode is presented.In particular,we use the pseudospectral method in the space coordinate direction as well as the fourth-oder Runge-Kutta method in the time direction for the time evolution,and then extract the quasinormal mode frequency by Prony method.On the other hand,we use the generalized eivenvalue method in the frequency domain analysis.As a result,we find that the results obtained by these two methods are in good agreement with each other.