Photon Rings Around Warped Black Holes

Abstract

The black hole photon ring is a prime target for upcoming space-based VLBI missions seeking to image the fine structure of astrophysical black holes. The classical Lyapunov exponents of the corresponding nearly bound null geodesics control the quasinormal ringing of a perturbed black hole as it settles back down to equilibrium, and they admit a holographic interpretation in terms of quantum Ruelle resonances of the microstate dual to the Kerr black hole. Recent work has identified a number of emergent symmetries related to the intricate self-similar structure of the photon ring. Here, we explore this web of interrelated phenomena in an exactly soluble example that arises as an approximation to the near-extremal Kerr black hole. The self-dual warped AdS${}_3$ geometry has a photon ring as well as $\mathsf{SL}(2,\mathbb{R})$ isometries and an exactly calculable quasinormal mode (QNM) spectrum. We show explicitly that the geometric optics approximation reproduces the eikonal limit of the exact QNM spectrum, as well as the approximate "near-ring" wavefunctions. The $\mathsf{SL}(2,\mathbb{R})$ isometries are directly related to the emergent conformal symmetry of the photon ring in black hole images but are distinct from a recently discussed conformal symmetry of the eikonal QNM spectrum. The equivalence of the classical QNM spectrum -- and thus the photon ring -- to the quantum Ruelle resonances in the context of a spacetime with a putative holographic dual suggests that the photon ring of a warped black hole is indeed part of the black hole hologram.

26 pages, 1 figure

References in corpus (13)

• Warped AdS_3 Black Holes
• Quasinormal-mode spectrum of Kerr black holes and its geometric interpretation
• Black hole mass and angular momentum in topologically massive gravity
• Slow relaxation of rapidly rotating black holes
• Chaos in the black hole S-matrix
• Holography of the Photon Ring
• String Theory on Warped AdS_3 and Virasoro Resonances
• Hidden Conformal Symmetry and Quasi-normal Modes
• Spectroscopy of Extremal (and Near-Extremal) Kerr Black Holes
• Self-Dual Warped AdS${}_3$ Black Holes
• Quasinormal Modes of Self-Dual Warped AdS${}_3$ Black Hole in Topological Massive Gravity
• A definition of primary operators in $J\bar{T}$-deformed CFTs
• Separating metric perturbations in near-horizon extremal Kerr

Cited by in corpus (11)

• Ladder Symmetries of Black Holes and de Sitter Space: Love Numbers and Quasinormal Modes
• The Black Hole Explorer: Photon Ring Science, Detection and Shape Measurement
• Black hole bulk-cone singularities
• On emergent conformal symmetry near the photon ring
• $SL(2,R)\times U(1)$ symmetry and quasinormal modes in the self-dual warped AdS black hole
• Static spheres and Aschenbach effect for black holes in massive gravity
• Quasinormal Corrections to Near-Extremal Black Hole Thermodynamics
• pp-Waves and the Hidden Symmetries of Black Hole Quasinormal Modes
• Hidden conformal symmetries for black holes in modified gravity
• Lumos Extrema
• Strong gravitational lensing of a five-dimensional charged, equally rotating black hole with a cosmological constant