标题： 新的数值方法用于评估Teukolsky方程的齐次解 显示英文标题

标题： New Numerical Methods to Evaluate Homogeneous Solutions of the Teukolsky Equation

摘要： 我们讨论了一种数值方法来计算Teukolsky方程的同质解，Teukolsky方程是黑洞摄动方法的基本方程。我们使用了由Mano、Suzuki和Takasugi发展的形式体系，在这个体系中，径向Teukolsky方程的同质解可以用两种特殊函数级数的形式表示，并且推导出了渐近振幅的公式。尽管这种方法以前的应用仅限于同质解的解析评估，但我们发现它也适用于数值计算。我们还发现，“重整化角动量参数”$\nu$只能在每个$l,m$对应的$\omega$的有限区域内找到（这里，$\omega$是角频率，$l$和$m$分别是自旋权值球面谐波的度和阶），如果我们假设$\nu$是实数的话。我们还计算了由紧凑星在旋转黑洞赤道面上的圆轨道诱导的引力波通量。 我们发现，能量流的相对误差约为$10^{-14}$，这比通常的数值积分方法得到的结果小得多。 显示英文摘要

摘要： We discuss a numerical method to compute the homogeneous solutions of the Teukolsky equation which is the basic equation of the black hole perturbation method. We use the formalism developed by Mano, Suzuki and Takasugi, in which the homogeneous solutions of the radial Teukolsky equation are expressed in terms of two kinds of series of special functions, and the formulas for the asymptotic amplitudes are derived explicitly.Although the application of this method was previously limited to the analytical evaluation of the homogeneous solutions, we find that it is also useful for numerical computation. We also find that so-called "renormalized angular momentum parameter", $\nu$, can be found only in the limited region of $\omega$ for each $l,m$ if we assume $\nu$ is real (here, $\omega$ is the angular frequency, and $l$ and $m$ are degree and order of the spin-weighted spheroidal harmonics respectively). We also compute the flux of the gravitational waves induced by a compact star in a circular orbit on the equatorial plane around a rotating black hole. We find that the relative error of the energy flux is about $10^{-14}$ which is much smaller than the one obtained by usual numerical integration methods.