Quasi-normal Modes Of Electromagnetic Field On The Background Of Kerr-Newman Black Hole

Since black holes have been predicted in General Relativity, scientists have done a lot of job to reveal the nature of black hole in theory and observation. Because of its characteristics, we can not detect black hole directly. Even so, we still have some indirect methods. Quasi-normal mode (QNM), one of indirect methods, is a kind of oscillation or evolution modes of a perturbed field. The idea of QNM is that after the initial perturbation, there is QNM ringing outside black hole. The frequencies and damping times of the ringing are insensitive to initial perturbation, but varies with different characteristic parameters of black hole such as mass, charge and angular momentum which can help us to identify the existence of black hole and reveal its nature. Although the study on QNM is in the phase of theory, the detection of QNM is expected to be realized through gravitational wave observation. This paper is divided into four sections to discuss the black hole and QNM, especially QNM about electromagnetic field on the background of Kerr-Newman (K-N) black hole. The paper is organized as follows:In Section One, firstly we review the process of black holes'formation and development of black hole theory and then present some ways about black holes'indirect observations and analyze their disadvantages.In Section Two, we introduce the origin of QNM study and present QNM's definition and characteristic and then analyze the feasibility of QNM's observation.In Section Three, we show two mathematical methods on QNM's study with two examples and then briefly introduce two common calculation methods on QNM.In Section four, the main body of our work, firstly we assume an electromagnetic perturbation around K-N black hole and then starting with Maxwell equation, we derive the wave equation obeyed by electromagnetic perturbation. Using numerical computation, we present several pictures to show the evolution of electromagnetic field and then analyze characteristics of QNM about electromagnetic field on the background of K-N black hole. Of course, the physical meaning is mentioned.