
Abstract 
1 
Introduction 

1.1 
General 

1.2 
PostNewtonian expansion of
gravitational waves 

1.3 
Linear perturbation theory of black
holes 

1.4 
Brief historical notes 
2 
Basic Formulae for the Black Hole
Perturbation 

2.1 
Teukolsky formalism 

2.2 
Chandrasekhar–Sasaki–Nakamura
transformation 
3 
PostNewtonian Expansion of the Regge–Wheeler
Equation 

3.1 
Basic assumptions 

3.2 
Horizon solution; 

3.3 
Outer
solution; 

3.4 
More on the inner boundary condition of the outer
solution 

3.5 
Structure of the ingoing wave function to 
4 
Analytic
Solutions of the Homogeneous Teukolsky Equation by Means of the Series
Expansion of Special Functions 

4.1 
Angular eigenvalue 

4.2 
Horizon solution in
series of hypergeometric functions 

4.3 
Outer solution as a series of Coulomb
wave functions 

4.4 
Matching of horizon and outer solutions 

4.5 
Low frequency
expansion of the hypergeometric expansion 

4.6 
Property of 
5 
Gravitational
Waves from a Particle Orbiting a Black Hole 

5.1 
Circular orbit around a
Schwarzschild black hole 

5.2 
Circular orbit on the equatorial plane around
a Kerr black hole 

5.3 
Waveforms in the case of circular orbit 

5.4 
Slightly
eccentric orbit around a Schwarzschild black hole 

5.5 
Slightly eccentric
orbit around a Kerr black hole 

5.6 
Circular orbit with a small inclination
from the equatorial plane around a Kerr black hole 

5.7 
Absorption of
gravitational waves by a black hole 

5.8 
Adiabatic evolution of Carter
constant for orbit with small eccentricity and small inclination angle
around a Kerr black hole 

5.9 
Adiabatic evolution of constants of motion
for orbits with generic inclination angle and with small eccentricity
around a Kerr black hole 
6 
Conclusion 
7 
Acknowledgements 

References 

Footnotes 

Updates 

Tables 