Holographic Einstein Ring of a Charged AdS Black Hole

TL;DR

This paper explores the properties of Einstein rings formed by complex scalar fields around charged AdS black holes, revealing temperature-dependent behaviors and universal features linked to high-energy modes in strongly coupled systems with gravity duals.

Contribution

It demonstrates that the Einstein ring radius remains unaffected by chemical potential and uncovers a temperature-dependent increase at low temperatures, highlighting universal behaviors in holographic models.

Findings

Einstein ring radius is independent of chemical potential.

The ring's radius increases at low temperatures.

The ring is well described by the photon sphere in geometric optics.

Abstract

Taking into account that the real quantum materials are engineered generically at a finite chemical potential, we investigate the Einstein ring structure for the lensed response of the complex scalar field as a probe wave on the charged AdS black hole in the context of AdS/CFT. On the one hand, we find that the resulting Einstein ring radius has no variation with the chemical potential, which is similar to the behavior for the weakly interacting quantum system. On the other hand, not only can such a ring exist well within the screen, but also the temperature dependence of its radius exhibits a distinct feature in the sense that it displays an appreciable increase at low temperatures while the ring keeps unchanged right at the edge of the screen for the weakly interacting system. Note that such a Einstein ring emerges in the large frequencies and can be well captured by the photon sphere away from the black hole horizon in the geometric optics approximation, thus such a distinct feature may be regarded as a universal behavior associated with the high energy modes of the strongly coupled system which has a gravity dual.