Stable photon orbits in stationary axisymmetric spacetimes with an electromagnetic field and a cosmological constant

Stable light rings, which are associated with spacetime instabilities, are known to exist in fourdimensional stationary axisymmetric spacetimes that solve the Einstein-Maxwell equations (so-called electrovacuum solutions, with Faraday tensor F-mu nu not equal 0 0); however, they are not permitted in pure vacuum (F-mu nu = 0). In this work, we extend this result to spacetimes with a nonzero cosmological constant A. In particular, we demonstrate that stable light rings are permitted in A-electrovacuum (F-mu nu not equal 0, Lambda not equal 0), but ruled out in A-vacuum (F-mu nu = 0, Lambda not equal 0).