Lux in obscuro: Photon Orbits of Extremal Black Holes Revisited

TL;DR

This paper investigates photon orbits near extremal black holes, showing stability of horizon photon spheres in certain cases and instability in others, with detailed analysis of Kerr-Newman black holes.

Contribution

It provides a general proof of stable photon spheres at extremal horizons for static spherically symmetric black holes and clarifies the stability properties of photon orbits in Kerr and Kerr-Newman black holes.

Findings

Stable photon sphere at extremal horizon for static spherically symmetric black holes.

In Kerr black holes, photon orbits on the horizon are unstable in the Doran frame.

Kerr-Newman black holes can have two equatorial photon orbits with different stability properties.

Abstract

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.