Solution
= Solution
The Killing <vectors> $\partial_t$ and $\partial_\phi$ give conserved specific energy and <angular momentum>,
$$
E=\left(1-\frac{2m}{r}\right)\dot t,
\qquad
h=r^2\dot\phi.
$$
The normalization $g_{\mu\nu}\dot x^\mu\dot x^\nu=-1$ then rearranges to
$$
\frac12\dot r^2-\frac{m}{r}+\frac{h^2}{2r^2}-\frac{mh^2}{r^3}
=\frac{E^2-1}{2},
$$
so the displayed radial energy is also constant. This is the <effective potential for timelike Schwarzschild geodesics>.