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A large class of spherically symmetric static extremal black hole spacetimespossesses a stable null photon sphere on their horizons. For the extremalKerr-Newman family, the photon sphere only really coincides with the horizon inthe sense clarified by Doran. The condition under which photon orbit is stableon an asymptotically flat extremal Kerr-Newman black hole horizon has recentlybeen clarified; it is found that a sufficiently large angular momentumdestabilizes the photon orbit, whereas electrical charge tends to stabilize it.We investigated the effect of a negative cosmological constant on thisobservation, and found the same behavior in the case of an extremalasymptotically Kerr-Newman-AdS black holes in (3+1)-dimensions. In(2+1)-dimensions, in the presence of electrical charge, the angular momentumnever becomes large enough to destabilize the photon orbit. We comment on theinstabilities of black hole spacetimes with a stable photon orbit.

Lux in obscuro II: Photon Orbits of Extremal AdS Black Holes Revisited