标题： 弯曲黑洞周围的光子环 显示英文标题

标题： Photon Rings Around Warped Black Holes

摘要： 黑洞光子环是即将开展的空间基VLBI任务的目标，这些任务旨在成像天体黑洞的精细结构。 相应近束缚零测地线的经典李雅普诺夫指数控制扰动黑洞恢复到平衡状态时的准正则鸣响，并且它们在量子Ruelle共振方面具有全息解释，这些共振对应于与克尔黑洞对偶的微观态。 近期的研究识别出与光子环复杂自相似结构相关的若干涌现对称性。 在此，我们探讨了一个精确可解的例子，该例子作为近极端克尔黑洞的近似而出现。 自对偶的扭曲AdS$_3$几何具有光子环以及$\mathsf{SL}(2,\mathbb{R})$等距对称性以及一个精确可计算的准正则模（QNM）谱。 我们明确展示了几何光学近似再现了精确QNM谱的eikonal极限以及近环的近似“环附近”波函数。 $\mathsf{SL}(2,\mathbb{R})$等距对称性直接与黑洞图像中光子环的涌现共形对称性相关，但不同于最近讨论的eikonal QNM谱的共形对称性。 在具有假想全息对偶时空的背景下，经典QNM谱（因此也是光子环）与量子Ruelle共振的等价性表明，扭曲黑洞的光子环确实是黑洞全息图的一部分。 显示英文摘要

摘要： 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.