On emergent conformal symmetry near the photon ring

TL;DR

This paper explores the emergent conformal symmetry near the photon ring in warped spacetime, introducing a new algebraic construction that links quasinormal modes to the phase space of the photon ring.

Contribution

It proposes a novel $sl(2,R)_{QNM}$ symmetry construction and relates it to the near-ring isometry group, advancing understanding of near-ring conformal structures.

Findings

Each eikonal QNM family forms a highest-weight representation of $sl(2,R)_{QNM}$

The $sl(2,R)_{QNM}$ algebra relates to the near-ring isometry group $sl(2,R)_{ISO}$

The coherent state space of $sl(2,R)_{QNM}$ matches the photon ring's phase space

Abstract

In this note we revisit the emergent conformal symmetry in the near-ring region of warped spacetime. In particular, we propose a novel construction of the emergent near-ring $sl(2,R)_{\text{QNM}}$ symmetry. We show that each eikonal QNM family falls into one highest-weight representation of this algebra, and $sl(2,R)_{\text{QNM}}$ can be related to the near-ring isometry group $sl(2,R)_{\text{ISO}}$ in a simple way. Furthermore we find that the coherent state space of $sl(2,R)_{\text{QNM}}$ can be identified with the phase space of the photon ring.