by Liu Yuk Tung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 144-150) and index. / by Liu Yuk Tung. / Contents --- p.i / List of Figures --- p.v / List of Tables --- p.vii / Abstract --- p.viii / Acknowledgements --- p.ix / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Gravitational Wave Astronomy --- p.1 / Chapter 1.2 --- Quasinormal Modes of Black Holes --- p.2 / Chapter 1.3 --- Objective and Outline of this Thesis --- p.4 / Chapter Chapter 2. --- Perturbations of Schwarzschild Black Holes --- p.7 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Weak Fields in the Schwarzschild Background --- p.8 / Chapter 2.3 --- Gravitational Perturbation of Schwarzschild Black Holes --- p.10 / Chapter 2.4 --- Scattering of Waves in a Schwarzschild Background --- p.12 / Chapter 2.5 --- Quasinormal Modes --- p.14 / Chapter Chapter 3. --- Green's Function Analysis --- p.16 / Chapter 3.1 --- Introduction --- p.16 / Chapter 3.2 --- Formalism --- p.17 / Chapter 3.3 --- The Signal at Early Time --- p.19 / Chapter 3.4 --- Quasinormal Ringings --- p.20 / Chapter 3.4.1 --- QNM spectrum of Schwarzschild Black Holes --- p.21 / Chapter 3.4.2 --- QNM spectrum of Kerr Black Holes --- p.23 / Chapter 3.5 --- Late Time Behavior --- p.24 / Chapter 3.6 --- Completeness of Quasinormal Modes --- p.25 / Chapter Chapter 4. --- Analytic Solutions of Regge-Wheeler Equation --- p.28 / Chapter 4.1 --- Introduction --- p.28 / Chapter 4.2 --- "Analytic Solutions for f(w, r) and g(w, r)" --- p.29 / Chapter 4.3 --- "Numerical Calculation of Leaver's series for(w, r)" --- p.32 / Chapter Chapter 5. --- Born Series --- p.36 / Chapter 5.1 --- Introduction --- p.36 / Chapter 5.2 --- Potentials with Exponential Tails --- p.37 / Chapter 5.2.1 --- Born Series Solution --- p.37 / Chapter 5.2.2 --- Poles in complex w plane --- p.38 / Chapter 5.3 --- Born Series Solution of Regge-Wheeler Potential --- p.39 / Chapter Chapter 6. --- Complex Integration --- p.44 / Chapter 6.1 --- Introduction --- p.44 / Chapter 6.2 --- Stokes and Anti-Stokes line --- p.45 / Chapter 6.3 --- Integration in the Complex Plane --- p.47 / Chapter 6.4 --- Stokes Phenomenon --- p.49 / Chapter 6.5 --- Integration of Regge-Wheeler Equation --- p.52 / Chapter Chapter 7. --- Semi-Analytic Method --- p.59 / Chapter 7.1 --- Introduction --- p.59 / Chapter 7.2 --- Application to Schwarzschild Black Holes --- p.60 / Chapter 7.3 --- Prospect of Application to Relativistic Stars --- p.63 / Chapter Chapter 8. --- Logarithmic Perturbation Theory --- p.65 / Chapter 8.1 --- Introduction --- p.65 / Chapter 8.2 --- Review on the Logarithmic Perturbation Theory --- p.67 / Chapter 8.3 --- General Properties of the Frequency Shift --- p.69 / Chapter 8.3.1 --- Open Systems in General --- p.69 / Chapter 8.3.2 --- Schwarzschild black holes --- p.72 / Chapter Chapter 9. --- The Shell Model of Dirty Black Holes --- p.78 / Chapter 9.1 --- Introduction --- p.78 / Chapter 9.2 --- The Master Equation --- p.79 / Chapter 9.3 --- Evaluation of Perturbation Formulas --- p.81 / Chapter 9.3.1 --- First Order Perturbation --- p.81 / Chapter 9.3.2 --- Second Order Perturbation --- p.84 / Chapter 9.4 --- Exact Calculation of QNMs of the Shell Model --- p.87 / Chapter 9.5 --- Comparison of Perturbation Calculation with Exact Result --- p.89 / Chapter 9.5.1 --- Dependence on μ and convergence --- p.89 / Chapter 9.5.2 --- Dependence on shell position --- p.91 / Chapter Chapter 10. --- Perturbations of Kerr Black Holes --- p.96 / Chapter 10.1 --- Introduction --- p.96 / Chapter 10.2 --- Teukolsky Equations --- p.96 / Chapter 10.3 --- The Radial Teukolsky Equation --- p.98 / Chapter 10.4 --- Superradiant Scattering --- p.100 / Chapter Chapter 11. --- Quasinormal Modes of Kerr Black Holes --- p.102 / Chapter 11.1 --- Introduction --- p.102 / Chapter 11.2 --- Angular Teukolsky Equation --- p.103 / Chapter 11.3 --- Born series solution --- p.104 / Chapter 11.4 --- Complex Integration of Teukolsky Equation --- p.106 / Chapter 11.5 --- The Semi-Analytic Method --- p.107 / Chapter Chapter 12. --- Conclusion --- p.114 / Chapter 12.1 --- Summary of Our Work --- p.114 / Chapter 12.2 --- Outlook --- p.116 / Appendix A. The Expansion Coefficients Vk for Black-Hole Potentials --- p.118 / Chapter A.1 --- Expansion of Regge-Wheeler Potential --- p.118 / Chapter A.2 --- Expansion of Teukolsky Potential --- p.120 / "Appendix B. Asymptotic Expression for g(w,r)" --- p.125 / Chapter B.l --- Regge-Wheeler Equation --- p.125 / Chapter B.2 --- Radial Teukolsky Equation --- p.126 / Appendix C. Numerical Derivatives and Root Searching Algorithm --- p.127 / Chapter C.1 --- Numerical Derivatives --- p.127 / Chapter C.2 --- Root Searching Algorithm --- p.130 / Appendix D. Derivation of the Equations for the Shell Model --- p.132 / Chapter D.1 --- The Metric of the Shell Model --- p.132 / Chapter D.2 --- The Master Equation for Scalar Waves --- p.134 / Chapter D.3 --- The Dominant Energy Condition for the Shell Model --- p.136 / Appendix E. Leaver's Analytic Solution of Teukolsky Equation --- p.139 / Chapter E.l --- Angular Equation --- p.139 / Chapter E.2 --- Radial Equation --- p.140 / Appendix F. Teukolsky-Starobinsky Identities --- p.142 / Bibliography --- p.144 / Index --- p.151
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_321969 |
| Date | January 1997 |
| Contributors | Liu, Yuk Tung., Chinese University of Hong Kong Graduate School. Division of Physics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, ix, 152 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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