Chapter 1. Black Hole Perturbation

We present analytic calculations of gravitational waves from a particleorbiting a black hole. We first review the Teukolsky formalism for dealing withthe gravitational perturbation of a black hole. Then we develop a systematicmethod to calculate higher order post-Newtonian corrections to thegravitational waves emitted by an orbiting particle. As applications of thismethod, we consider orbits that are nearly circular, including exactly circularones, slightly eccentric ones and slightly inclined orbits off the equatorialplane of a Kerr black hole and give the energy flux and angular momentum fluxformulas at infinity with higher order post-Newtonian corrections. Using adifferent method that makes use of an analytic series representation of thesolution of the Teukolsky equation, we also give a post-Newtonian expandedformula for the energy flux absorbed by a Kerr black hole for a circular orbit.Comment: 120 pages ptptex file. To appear in Progress of Theoretical Physics Supplement No.128 (1997) `Perturbative and Numerical Approaches to Gravitational Radiation