Photon Rings Around Warped Black Holes

TL;DR

This paper investigates the photon ring structure around warped black holes, demonstrating how classical and quantum resonances relate through holography, and providing an exactly solvable model that links geometric optics, quasinormal modes, and emergent symmetries.

Contribution

It presents an exactly solvable warped AdS3 black hole model that connects photon rings, quasinormal modes, and holographic dualities, revealing the role of symmetries and resonances.

Findings

Geometric optics reproduces the eikonal limit of QNM spectrum.

Emergent conformal symmetry relates to photon ring structure.

Photon ring spectrum matches quantum Ruelle resonances in holographic context.

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.