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.

中文翻译：

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引力辐射的解析黑洞扰动方法。

我们基于黑洞扰动理论，回顾了用于执行绕牛顿的引力波的牛顿扩展的解析方法，该粒子绕大而紧凑的物体运行。存在执行牛顿后扩展的两种不同方法。两者均基于Teukolsky方程。一种方法是将Teukolsky方程转换为Regge-Wheeler型方程，该方程在平面空间极限内简化为标准的Klein Gordon方程，而另一种方法（由Mano，Suzuki和Takasugi引入， Teukolsky方程式直接以其原始形式使用，前者的优点是直观上很容易理解各种弯曲空间效应是如何起作用的。当人们接受越来越高的后牛顿阶数时，它变得越来越复杂。相反，后者的优点是可以相对容易地实现对较高的后牛顿阶的系统计算，但否则，它是如此的数学，以至于难以理解高阶项的相互作用。在本文中，我们回顾了这两种方法，以便可以清楚地看出它们的优缺点。我们还回顾了绕黑洞运行的粒子发射的引力辐射的一些计算结果。我们将对这两种方法进行回顾，以便可以清楚地看到它们的优缺点。我们还回顾了绕黑洞运行的粒子发射的引力辐射的一些计算结果。我们将对这两种方法进行回顾，以便可以清楚地看到它们的优缺点。我们还回顾了绕黑洞运行的粒子发射的引力辐射的一些计算结果。