Quasinormal Modes And Area Spectrum Of Dirac Field In Einstein-Born-Infeld Dilaton Black Hole

As is known to all,Einstein’s general theory of relativity is a theory related to time,space and gravity.The existence of energy-momentum(that is,matter)causes the curvature of four-dimensional space-time,and black holes are the inevitable product of curved space-time.In general relativity,the properties of all asymptotically flat steadystate black holes of the Einstein-Maxwell equations of gravity and electromagnetism can only be determined by three parameters(mass M,charge Q,and angular momentum J),which is called the no-hair theorem.When a black hole is perturbed,the response will undergo three stages.The first stage is the initial fluctuation stage.The second one is the decaying oscillation stage,which is called quasinormal modes(QNMs)stage.And the last stage corresponds to late time decay.The quasinormal modes stage is independent of the initial perturbation of black hole,so it can reflect the characteristics of the black hole space-time and can provide information about the black hole.Since the quasinormal frequencies is related to the properties of the three parameters of the black hole,such as M,Q,and J,they can directly identify the space-time parameters.In September 2015,gravitational waves(GWs)was confirmed to exist.The first gravitational wave event observed was caused by the last moment radiation of the merging of two black holes.In this context,QNMs of the black hole space-time are related with the ringdown phase of GWs.Based on the physics of Einstein’s theory of general relativity,studying QNMs can provide us with many new clues,and we can understand some unique properties of black holes through QNMs.In this paper,we study the quasinormal spectrum of Einstein-BornInfeld dilaton(EBID)black hole in the space-time background,discuss the influence of the Dirac field as a disturbance source on the stability of the black hole,and analyze the relationship between the QNMs and some characteristic parameters of EBID black hole.The structure of this paper is divided into five chapters.In section 1,some basic concepts of black hole theory are briefly introduced,including the proposal of black holes and the thermodynamics law of black holes.Then the proposal,concept,and research value of the black hole quasinormal modes are expounded.In section 2,we mainly introduce the research background of EBID gravitational theory and its static spherically symmetric solution,and the radial decoupled Dirac equations and corresponding wave equation in the EBID spacetime are obtained by using Newman-Penrose formalism.In section 3,we solve the radial equation exactly and the QNMs is obtained under boundary conditions.We find that the quasinormal frequencies are purely imaginary which means that this kind of black hole is very stable,and discuss the relationship between the quasinormal frequencies and EBID black hole space-time background parameters.In the next section 4,we calculated the area spectrum of the EBID black hole based on the obtained quasinormal frequencies,we find that the area spacing of the black hole is described by ?Amin= 8π which supports Bekenstein’s conjecture.The last part is the summary of our research content and the prospect for the follow-up work.