Lumos Extrema

TL;DR

This paper investigates photon trajectories and quasi-normal modes around charged black holes in AdS spacetimes, revealing how the photon ring probes near-horizon physics and identifying new relaxation time-scales in the dual field theory.

Contribution

It introduces a novel $ ext{i} \e$-prescription for the JWKB approximation, analyzes the photon ring in near-extremal limits, and computes quasi-normal modes revealing new relaxation dynamics.

Findings

Photon ring properties depend on spacetime dimensions and particle charge.

A new time-scale of relaxation governed by chemical potential is identified.

The $ ext{i} \e$-prescription simplifies analysis of superradiant instabilities.

Abstract

We consider trajectories of massless particles in the presence of charged black holes in asymptotically AdS spacetimes in arbitrary dimensions. We study the properties of the photon ring in the (near-)extremal limit and show that the photon ring can probe the near-horizon region in two different scenarios: in high enough number of spacetime dimensions or when the massless particle carries an electric charge. We propose a simple $\mathrm{i} \epsilon$-prescription for implementing the JWKB approximation and show its utility in various contexts. We calculate the quasi-normal modes for charged fields in the eikonal limit and show the emergence of a new time-scale of relaxation in the dual field theory side. In the near-extremal limit, we show generally that the time-scale of decay of the perturbations is governed by the chemical potential. We also verify our analytical results numerically. The $\mathrm{i} \epsilon$-prescription allows us to study the superradiant modes and the associated instabilities in the eikonal limit easily. We comment on some related aspects regarding near-extremal black holes.