Light rings of five-dimensional geometries

Understand

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.