Analytic black hole perturbation approach to gravitational radiation

TL;DR

This paper reviews analytic methods based on black hole perturbation theory for calculating gravitational waves from particles orbiting massive bodies, comparing two approaches and summarizing recent results in gravitational radiation modeling.

Contribution

It provides a comprehensive comparison of two post-Newtonian expansion methods using the Teukolsky equation, highlighting their advantages and limitations.

Findings

Both methods successfully compute gravitational radiation.

The Regge-Wheeler approach offers intuitive understanding.

The Mano, Suzuki, Takasugi method facilitates higher-order calculations.

Abstract

We review analytic methods to perform the post-Newtonian expansion of gravitational waves induced by a particle orbiting a massive compact body, based on the black hole perturbation theory. There exist two different methods of the post-Newtonian expansion. Both are based 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 were introduced by Mano, Suzuki and Takasugi relatively recently, the Teukolsky equation is directly used in its original form. The former has an advantage that it is intuitively easy to understand how various curved space effects come into play. However, it becomes increasingly complicated when one goes on to higher and higher post-Newtonian orders. In contrast, the latter has an advantage that a systematic calculation to higher post-Newtonian orders is relatively easily implementable, but otherwise 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 clearly seen. We also review some results of calculations of gravitational radiation emitted by a particle orbiting a black hole.