# 图科斯基方程

${\displaystyle \left[{\frac {r^{2}+a^{2}}{\Delta }}-a^{2}\sin ^{2}\theta \right]{\frac {\partial ^{2}\psi }{\partial t^{2}}}+{\frac {4Mar}{\Delta }}{\frac {\partial ^{2}\psi }{\partial t\partial \phi }}+\left[{\frac {a^{2}}{\Delta }}-{\frac {1}{\sin ^{2}\theta }}\right]{\frac {\partial ^{2}\psi }{\partial \phi ^{2}}}-\Delta ^{-s}{\frac {\partial }{\partial r}}\left(\Delta ^{s+1}{\frac {\partial \psi }{\partial r}}\right)}$
${\displaystyle -{\frac {1}{\sin \theta }}{\frac {\partial }{\partial \theta }}\left(\sin \theta {\frac {\partial \psi }{\partial \theta }}\right)-2s\left[{\frac {a(r-M)}{\Delta }}+{\frac {i\cos \theta }{\sin ^{2}\theta }}\right]{\frac {\partial \psi }{\partial \phi }}}$
${\displaystyle -2s\left[{\frac {M\left(r^{2}-a^{2}\right)}{\Delta }}-r-ia\cos \theta \right]{\frac {\partial \psi }{\partial t}}+s\left[s\cot ^{2}\theta -1\right]\psi =4\pi \Sigma {\mathcal {T}}}$

## 参考资料

1. ^ Teukolsky S A. Perturbations Of A Rotating Black Hole. 1. Fundamental Equations For Gravitational Electromagnetic, And Neutrino Field Perturbations. Astrophys. J. 1973, 185: 635 [2008-02-12]. （原始内容存档于2017-11-14）.