Calculate Regge-Wheeler Variables

$$\begin{eqnarray*} c_1^{\times lm} &=& \frac{1}{l(l+1)} \int \frac{\gamma_{\hat{... ..._{lm,\theta \phi }-\cot\theta Y^*_{lm,\phi }) \right\}d\Omega \end{eqnarray*}$$

where

$$\gamma_{\hat{r}\hat{r}} = \frac{\partial r}{\partial \hat{r}} \frac{\partial r}{\partial \hat{r}} \gamma_{rr}$$ (part3125)

$$\gamma_{\hat{r}\theta } = \frac{\partial r}{\partial \hat{r}} \gamma_{r\theta }$$ (part3126)

$$\gamma_{\hat{r}\phi } = \frac{\partial r}{\partial \hat{r}} \gamma_{r\phi }$$ (part3127)