Light rings of five-dimensional geometries

We study massless geodesics near the photon-spheres of a large family of solutions of Einstein-Maxwell theory in five dimensions, including BHs, naked singularities and smooth horizon-less JMaRT geometries obtained as six-dimensional uplifts of the five-dimensional solution. We find that a light ring of unstable photon orbits surrounding the mass center is always present, independently of the existence of a horizon or singularity. We compute the Lyapunov exponent, characterizing the chaotic behaviour of geodesics near the `photon-sphere' and the time decay of ring-down modes dominating the response of the geometry to perturbations at late times. We show that, for geometries free of naked singularities, the Lyapunov exponent is always bounded by its value for a Schwarzschild BH of the same mass.