论文标题
在特定情况下
Exact solutions of the angular Teukolsky equation in particular cases
论文作者
论文摘要
在这项工作中，我们提出了一个新方案，以解决特定情况的Angular Teukolsky方程：$ M = 0，S = 0 $。我们首先将此方程式转换为汇合的heun微分方程，然后构造wronskian的决定因素以计算特征值和归一化的特征功能。我们发现，较大$ l $的特征值大约由$ _ {0} {a_ {a_ {l0}} \ of [l（l + 1） - τ_{r}^2/2] - i \;τ_;τ_{i}^2 $，带有任意的$ f.^2 $基态的角概率分布（APD）以$τ_r^2> 0 $向北和南极移动，但以$τ_r^2 \ leq0 $汇总到赤道。但是，我们还注意到，无论选择$τ^2 $，大型角动量$ l $的APD总是向北极和南极移动。
In this work, we propose a new scheme to solve the angular Teukolsky equation for the particular case: $m=0, s=0$. We first transform this equation to a confluent Heun differential equation and then construct the Wronskian determinant to calculate the eigenvalues and normalized eigenfunctions. We find that the eigenvalues for larger $l$ are approximately given by $_{0}{A_{l0}} \approx [l(l + 1) - τ_{R}^2/2] - i\;τ_{I}^2/2$ with an arbitrary $τ^2=τ_R^2 + i\,τ_{I}^2$. The angular probability distribution (APD) for the ground state moves towards the north and south poles for $τ_R^2>0$, but aggregates to the equator for $τ_R^2\leq0$. However, we also notice that the APD for large angular momentum $l$ always moves towards the north and south poles , regardless the choice of $τ^2$.
