The null circular geodesic outside the spherically symmetric asymptotically flat hairy black hole is not stable

Abstract

In this study, we explicitly prove that the null circular orbit outside the spherically symmetric asymptotically flat hairy black hole is not stable. Although, if there is more than one external light ring at least one of them is stable. The existence of such geodesics has been proved in the recent work of Hod as well as Peng whereas its stability was left uncommented.