Dirac Quasinormal Modes In The Spherically Symmetric Black Holes Spacetimes

As an important issue of black hole physics, the study of black hole’s quasinormal modes frequencies(QNMs) can reveal the evolution of material field’s wave packet after disturbing the black holes. As the black hole’s “features voice”, the QNMs are regarded as a powerful evidence of black hole existence. If gravitational waves are detected, then we can also through gravitational wave test to detect the existence of black holes. Therefore, he QNMs can help us further understand the characteristics of black hole.In this thesis, we focus on the QNMs of black hole, and mainly discuss the Dirac disturbance impact on the stability of the black hole. The content is mainly composed of the following five parts: The first part is the introduction; In the second part, we study the Dirac field disturbance; The third and the fourth part respectively calculate the QNMs of regular black holes and f(R) black holes under Dirac field disturbance; Finally we make a summary and useful outlook.The detailed content is as follows: in the first chapter, we roughly introduce the development of the physics of black holes, the nature of the black hole, the research progress of the black hole’s QNMs, the calculation method of the black hole’s QNMs and the significance of black hole. In the second chapter, from Dirac equation in the curved space-time, a Schr?dinger equation of the black hole oscillation is obtained. In the third chapter, using the WKB approximation, massless and massive Dirac quasinormal modes(QNMs) are studied in spherically symmetric space-times. We analyze the relationships between QNM frequencies and the parameters(angular momentum number l, magnetic monopole charge ? and the mass of the ?eld m), discussed the condition of extreme black hole, and finally we use the finite difference method to find the relationship between the radial wave function and time. Then we illuminate the dynamical evolution of the massive Dirac ?eld. In the fourth chapter, we discussed two black holes deduced from the static f(R) gravitational theory: f(R)(Schwarzschild) black hole and f(R)-Maxwell black hole. We use the finite difference method to analyze the stability of the f(R) black holes, and de?ne the threshold range of f(R)(Schwarzschild) black hole and f(R)-Maxwell black hole. Meanwhile we study the impact of the angular quantum number values | k| on the f(R) black holes. Furthermore, under the Dirac perturbation, the stability of the f(R) solutions can be reflected in the manner of Dirac quasinormal modes(QNMs), we analyze the relationships between the QNM frequencies and the parameters(angular momentum number l, magnetic monopole charge ? and the mass of the ?eld m) in massless and in massive cases, by contrast to the classical black holes. The fifth chapter is the summary and outlook.