The Scattering Of The Acoustic Black Holes

The perturbations of black holes have been studied for many years.It is been well known that there are three stages during the evolution of the field perturbation in the black hole background: the initial outburst from the source of the perturbation,the quasi-normal oscillations and the asymptotic tails.The frequencies and damping time of the quasi-normal oscillations called “quasi-normal mode”(QNM)are determined only by the black hole's parameters and independent of the initial perturbations.QNM frequencies(QNMs)is one of the important and exciting themes in the black hole physics.The basic physics of acoustic black hole is this: A moving fluid will drag sound waves along with it,and if the speed of the fluid ever becomes supersonic,then in the supersonic sound waves will never be able to fight their way back upstream.This implies the existence of a “dumb hole”,a region from which sound can not escape.The most effective way to study the acoustic black hole is to study its scattering.In the first chapter,we introduce the development of general relativity and black holes.Also,we introduce the development of QNM.In the second chapter,we adopt WKB approach to study the massive scalar fields and Dirac fields QNMs of Schwarchild black hole.In the third chapter,we present an analysis of scattering by a fluid-mechanical “black hole analogue”,known as the draining bathtub vortex: a two-dimensional flow that possesses both a sonic horizon and an ergoregion.By using classical mechanics method,We consider the scattering of a plane wave of fixed frequency impinging upon the vortex.At low frequency,we encounter a modified Aharonov-Bohm effect.At high frequencies,we observe regular “orbiting” oscillations in the scattering length,due to interference between contra-orbiting rays.Finally,we present approximate formulas for both effects.By calculating Quasi-normal modes,we found the real and imaginary part of the QN frequencies give the vibration frequency and the exponential damping frequency respectively.Summary of thesis and expectation of future are giving in chapter four.