Lumos Extrema

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.