Teukolsky方程II齐次解的新数值方法连分式方程的解
New Numerical Methods to Evaluate Homogeneous Solutions of the Teukolsky Equation II. Solutions of the Continued Fraction Equation
摘要：
我们调查的连分数方程的解决方案，我们确定“重整化角动量参数”，$ν$，在形式主义开发的Leaver和Mano，铃木，和Takasugi。在这种形式主义中，我们描述径向Teukolsky方程，这是黑洞扰动形式主义的基本方程的齐次解。我们发现，与以前的工作中所作的假设相反，解决方案，$ν$，成为复值为$ω$（角频率）变得大的每个$l$和$m$（度和阶的自旋加权球谐函数）。我们用两种方法比较了Kerr黑洞赤道平面上的圆形轨道上的粒子辐射引力波的功率，一种是用Mano-Suzuki-Takasugi形式和复$ν$，另一种是用直接的数值积分方法。我们发现，这两种方法产生一致的结果。这些事实证明了利用复解来确定Teukolsky方程齐次解的有效性。
英文摘要：
We investigate the solution of the continued fraction equation by which we determine "the renormalized angular momentum parameter", $ν$, in the formalism developed by Leaver and Mano, Suzuki, and Takasugi. In this formalism, we describe the homogeneous solutions of the radial Teukolsky equation, which is the basic equation of the black hole perturbation formalism. We find that, contrary to the assumption made in previous works, the solution, $ν$, becomes complex valued as $ω$ (the angular frequency) becomes large for each $l$ and $m$ (the degree and order of the spin-weighted spheroidal harmonics). We compare the power radiated by gravitational waves from a particle in a circular orbit in the equatorial plane around a Kerr black hole in two ways, one using the Mano-Suzuki-Takasugi formalism with complex $ν$ and the other using a direct numerical integration method. We find that the two methods produce consistent results. These facts prove the validity of using complex solutions to determine the homogeneous solutions of the Teukolsky equation.
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