T}^{\rightarrow}_{E lm}|^2\,.$$ Thus, in the limit $E\to 0$ we find $$R_{0lm} = \lim_{E \to 0}
{|{\cal T}^{\rightarrow}_{E lm}|^2}/{(2ME)}\,.
\label{res}$$

Next ${\cal T}^{\rightarrow}_{E lm}$ will be calculated. The equation satisfied by the function $q^{\rightarrow}_{\omega l}(r)\equiv (2M/r)
\varphi^{(1\rightarrow)}_{\omega l} (r)$ can be obtained from Eq. (\[varphi1\]) with $p=2$ as $$\frac{d\ }{dz} \left[(1-z^2)\frac{dq^{\rightarrow}_{\omega l}}{dz}\right]
+ \left[ l(l+1) - \frac{2}{z+1} - M^2\omega^2 \frac{(z+1)^3}{z-1}\right]
q^{\rightarrow}_{\omega l} = 0\,,  \label{equa}$$ where $z  \equiv r/M - 1$. For small $\omega$, the wave is almost completely reflected back to the horizon. This implies that $$\varphi^{(1\rightarrow)}_{\omega l} \approx 
- 2\sin [\omega (r^* -\tilde{r}_\omega)] 
\approx -2\omega r^* + {\rm const}.\;\;\;\;\; 
(r-r_H \ll \omega^2 r_H^3, \, |\omega r^*| \ll 1) \,,
\label{cond1}$$ where $\tilde{r}_\omega$ are constants. The minus sign has been inserted for later convenience. The Wheeler tortoise coordinate $r^*$ defined by Eq. (\[tortoise\]) is written in Schwarzschild spacetime as $$r^* = r + 2M\ln\left({r \over 2M} - 1\right)\,.$$ Thus, Eq. (\[cond1\]) can be written as $$\varphi^{(1\rightarrow)}_{\omega l}\approx
-4M\omega\ln(z-1)\, \;\;\;\;\;  
(r-r_H \ll \omega^2 r_H^3, \, |\omega r^*| \ll 1) \,. 
\label{cond2}$$ Now, Eq. (\[equa\]) can be solved explicitly for $\omega = 0$. By choosing the solution for $q^{\rightarrow}_{\omega l}$ such that $\varphi^{(1\rightarrow)}_{\omega l} = [r/(2M)]q^{\rightarrow}_{\omega l} $ tends to zero as 