Fine structure of the black hole photon ring

In the past few years, the Event Horizon Telescope has released the first close-up interferometric images of two supermassive black holes, M87* and SgrA*. It is believed that within these images is embedded a fine, yet-unresolved brightness enhancement called the photon ring. The ring is a universal consequence of extreme lensing by the black hole and thereby conveys information on its spacetime geometry, potentially providing a new independent avenue for future tests of general relativity in the strong-field regime. In the talk we will discuss the theory of the photon ring and its corresponding spacetime region, the photon shell, which defines a special codimension-two submanifold of the null-geodesic phase space and governs the universal lensing structure. For a Kerr black hole, we will describe the latter's symplectic geometry and discuss some potential consequences that follow from its detailed form.