  It has been shown in the literature that the event horizon of an extremal
asymptotically flat Reissner-Nordstrom black hole is also a stable photon
sphere. We further clarify this statement and give a general proof that this
holds for a large class of static spherically symmetric black hole spacetimes
with an extremal horizon. In contrast, in the Doran frame, an extremal
asymptotically flat Kerr black hole has an unstable photon orbit on the
equatorial plane of its horizon. In addition, we show that an extremal
asymptotically flat Kerr-Newman black hole exhibits two equatorial photon
orbits if a < M/2, one of which is on the extremal horizon in the Doran frame
and is stable, whereas the second one outside the horizon is unstable. For a >
M/2, there is only one equatorial photon orbit, located on the extremal
horizon, and it is unstable. There can be no photon orbit on the horizon of a
non-extremal Kerr-Newman black hole.
