Photon sphere and quasinormal modes in AdS/CFT

TL;DR

This paper analyzes the spectral properties of photon spheres in AdS Schwarzschild black holes, revealing unique quasinormal mode patterns that inform the structure of thermal holographic CFTs via the AdS/CFT correspondence.

Contribution

It provides a spectral analysis near the photon sphere, connecting quasinormal modes to boundary effects and predicting a special subsector in large angular momentum spectra of CFTs.

Findings

Quasinormal modes near the photon sphere reflect the AdS boundary.

Spectral patterns resemble solvable Schrödinger equations like the inverted harmonic oscillator.

Predicts a peculiar subsector in the large angular momentum spectrum of holographic CFTs.

Abstract

Photon spheres are the characteristic of general black holes, thus are a suitable touchstone for the emergence of gravitational spacetime in the AdS/CFT correspondence. We provide a spectral analysis of an AdS Schwarzschild black hole near its photon sphere. We find that quasinormal modes near the photon sphere reflect the AdS boundary, resulting in a peculiar spectral pattern. Our large angular momentum analysis owes to an analogue to solvable Schr\"odinger equations such as an inverted harmonic oscillator and the P\"oschl-Teller model, with a Dirichlet boundary condition. Through the AdS/CFT dictionary, it predicts the existence of a peculiar subsector in the large angular momentum spectrum of thermal holographic CFTs on a sphere.