We review the analytic methods used to perform the post-Newtonian expansion of gravitational waves induced by a particle orbiting a massive, compact body, based on black hole perturbation theory. There exist two different methods of performing the post-Newtonian expansion. Both are based on the Teukolsky equation. In one method, the Teukolsky equation is transformed into a Regge–Wheeler type equation that reduces to the standard Klein–Gordon equation in the flat-space limit, while in the other method (which was introduced by Mano, Suzuki, and Takasugi relatively recently), the Teukolsky equation is used directly in its original form. The former’s advantage is that it is intuitively easy to understand how various curved space effects come into play. However, it becomes increasingly complicated when one goes to higher and higher post-Newtonian orders. In contrast, the latter’s advantage is that a systematic calculation to higher post-Newtonian orders can be implemented relatively easily, but otherwise, it is so mathematical that it is hard to understand the interplay of higher order terms. In this paper, we review both methods so that their pros and cons may be seen clearly. We also review some results of calculations of gravitational radiation emitted by a particle orbiting a black hole.
Keywords: Teukolsky equation, Post-Newtonian expansion
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Since a Living Reviews in Relativity article may evolve over time, please cite the access <date>, which uniquely identifies the version of the article you are referring to:
Misao Sasaki and Hideyuki Tagoshi,
"Analytic Black Hole Perturbation Approach to Gravitational Radiation",
Living Rev. Relativity 6, (2003), 6. URL (cited on <date>):
|Title||Analytic Black Hole Perturbation Approach to Gravitational Radiation|
|Author||Misao Sasaki / Hideyuki Tagoshi|
|Date||accepted 5 September 2003, published 21 November 2003|
|Date||accepted 24 August 2010, published 14 September 2010|
|Changes||The main changes are new Sections 4.6, 5.3, 5.8, and 5.9, which show the progress since 2003. Added 46 new references.
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