Holography of the Photon Ring

TL;DR

This paper links classical Lyapunov exponents of photon orbits around black holes to quantum resonances in holography, revealing universal features of Kerr black hole spectroscopy with implications for observations.

Contribution

It establishes a connection between photon ring Lyapunov exponents and quantum Ruelle resonances, and identifies emergent conformal symmetries in Kerr phase space regions.

Findings

Lyapunov exponents equal quantum Ruelle resonances.

Emergent conformal symmetries constrain observational predictions.

Universal features of Kerr spectroscopy identified.

Abstract

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. The emergent conformal symmetries greatly constrain the observational predictions for the fine photon ring substructure around M87* and for quasinormal gravitational-wave ringdowns, as well as any proposal for a quantum holographic dual to the Kerr black hole. More generally, we hope that our identification of several universal features of Kerr spectroscopy provides a useful starting point for a bottom-up approach to holography for astrophysical black holes.