以狄拉克δ函数为源积分2+1波动方程的新方法
New method to integrate 2+1 wave equations with Dirac's delta functions as sources
摘要：
Kerr黑洞背景中的引力扰动在时域中不能分解为简单的张量谐波。在这里，我们只在方位角方向上进行模分解，并讨论了以二维Dirac $δ$ -函数作为表示绕一个大得多的黑洞运行的点粒子的源的标量扰动的（2+1）维Klein-Gordon微分方程.为了使这个方程适合于数值积分，我们明确地去除解析的奇异行为的源和计算相应的波形的全球有效源。
英文摘要：
Gravitational perturbations in a Kerr black hole background can not be decomposed into simple tensor harmonics in the time domain. Here, we make the mode decomposition only in the azimuthal direction and discuss the resulting (2+1)-dimensional Klein-Gordon differential equation for scalar perturbations with a two dimensional Dirac's $δ$-function as a source representing a point particle orbiting a much larger black hole. To make this equation amenable for numerical integrations we explicitly remove analytically the singular behavior of the source and compute a global effective source for the corresponding waveform.
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