Holography of the Photon Ring

Understand

Space-based next-generation interferometers propose to measure the Lyapunov exponents of the nearly bound geodesics that comprise the photon ring surrounding the black hole M87*.

• We argue that these classical Lyapunov exponents equal the quantum Ruelle resonances describing the late-time approach to thermal equilibrium of the quantum microstate holographically dual to any Kerr black hole such as M87*.
• Moreover, we identify "near-ring regions" in the phase space of fields propagating on Kerr that exhibit critical behavior, including emergent conformal symmetries.
• These are analogues for sub-extremal Kerr of the much-studied "near-horizon regions" of (near-)extremal black holes.