The Numerical Methods Of The Quasi-normal Mode Of Black Hole

An astronomical black hole that presents in the universe is always in a perturbed state.The initial moment of the black hole formation after the gravitational collapse of matter can also be described by a perturbed state of the black hole.So the study of the black hole perturbations theory has realistic and theoretical significance.The quasi-normal modes,which can be interpreted as the complex frequency of the perturbed field,first appear in the process of separating variables of this theory.We use three numerical methods(WKB method,generalized eigenvalue method,and continued fractions method)to calculate the quasi-normal modes.The comparison between different methods confirms the effectiveness and accuracy of our paper.We mainly promote the continued fractions method and propose a new numerical program that circumvents the difficulty of the derivation of the analytical 3-term recurrence formula in the continued fractions method.We study the quasi-normal modes of the charged scalar perturbations in the background of the Einstein-Maxwell-aether black hole to investigate the effect of different system parameters.Einstein-Maxwell-aether theory is a Lorentz violation beyond the general relativity,which includes an extra timelike vector field(aether)to interact with spacetime.At first,we demonstrate the results of three different methods for both uncharged and charged cases by tables.The accuracy is verified through the comparison of methods and the relative effects of the aether field are also given in the tables.Then we show the figures about the quasi-normal modes with varying the system parameters and the allowable regions of parameters of the second kind of aether black hole.We fully investigate the effect of parameters on the quasi-normal modes by these plots.We also study the quasi-resonance of Einstein-Maxwell-aether black holes.