The understanding of quasinormal modes
Date Issued
2006
Date
2006
Author(s)
Wu, Meng-Syun
DOI
en-US
Abstract
In this thesis, the physical origin of quasinormal modes is discussed. Traditionally, we can consider a wave equation (ex. Klein-Gordon equation) in the Schwarzschild background, and use the Wronskian of the two independent solutions to the equation in the Laplace picture to define the quasi-normal modes. However, this kind of definition seems to be less physical sense. Therefore we are attempted to use the scattering matrix or S-matrix to understand quasinormal modes. We find the poles of determinant of the S-matrix are equivalent to the zeros of the Wronskian in the Laplace picture. And then we use the scattering states to construct our wave function. We find we can just solve the wave equations with the proper initial conditions in the scattering problem, and then we can use the poles of the determinant of S-matrix to obtain the quasi-normal mode naturally. The wave function is physical, so definition S-matrix is of a more physical sense. Finally, we use Born approximation to obtain the large quasinormal modes in the case of potential barrier and Schwarzschild black hole. We get the not bad results in these cases.
Subjects
準正則模
史互茲黑洞
散射矩陣
波恩近似
quasinormal modes
Schwarzschild black hole
scattering matrix
Born approximation
Type
thesis
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