Light rings of five-dimensional geometries

TL;DR

This paper investigates light rings and photon-spheres in five-dimensional Einstein-Maxwell solutions, revealing universal presence of unstable photon orbits and bounding chaos measures by Schwarzschild black holes.

Contribution

It demonstrates the existence of light rings in various five-dimensional geometries, including horizonless and singular solutions, and analyzes their chaotic properties and stability bounds.

Findings

Unstable photon orbits are always present near the photon-sphere.

Lyapunov exponent is bounded by that of a Schwarzschild black hole.

Ring-down decay modes are characterized and computed.

Abstract

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.