Holography of the Photon Ring

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.

26 pages, 2 figures

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Cited by in corpus (5)

• Adaptive Analytical Ray Tracing of Black Hole Photon Rings
• Ladder Symmetries of Black Holes and de Sitter Space: Love Numbers and Quasinormal Modes
• Photon Rings Around Warped Black Holes
• Black hole mirages: electron lensing and Berry curvature effects in inhomogeneously tilted Weyl semimetals
• On emergent conformal symmetry near the photon ring