Solution
= Solution
For a nonradial <null geodesic>,
$$
V(r)=L^2\left(\frac1{r^2}-\frac{2m}{r^3}-H^2\right).
$$
It tends to $-\infty$ as $r\to0^+$, rises to one maximum, and tends to $-L^2H^2$ as $r\to\infty$. A <circular null geodesic> requires $V'(r)=0$, so
$$
-\frac2{r^3}+\frac{6m}{r^4}=0
\quad\Longrightarrow\quad
\boxed{r=3m}.
$$
Since $V''(3m)<0$, this <photon sphere> is unstable. Its energy satisfies $E^2=L^2(1/(27m^2)-H^2)$.