Lux in obscuro: Photon Orbits of Extremal Black Holes Revisited

Understand

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.