Holographic Einstein Ring of AdS Reissner Nordstr$\ddot{o}$m Black Holes with Euler Heisenberg Nonlinear Electrodynamics

TL;DR

This paper investigates the holographic Einstein ring structure of quantum corrected AdS Reissner Nordstr"om black holes influenced by Euler Heisenberg nonlinear electrodynamics, revealing how physical parameters affect the ring's morphology and size.

Contribution

It introduces a wave optics approach to analyze holographic Einstein rings in nonlinear electrodynamics black holes within AdS/CFT, highlighting parameter effects on observable boundary features.

Findings

Ring radius decreases with source position, wave frequency, and chemical potential.

Ring radius increases with electric charge and temperature.

Quantum correction parameter has negligible effect on the ring.

Abstract

This study, situated within the framework of the AdS/CFT correspondence, employs wave optics methods to investigate the Einstein ring structure of quantum corrected AdS Reissner Nordstr$\ddot{o}$m black holes governed by Euler Heisenberg nonlinear electrodynamics. A wave source placed on the AdS boundary yields a response function on the antipodal side, from which a virtual optical system with a convex lens reconstructs the holographic image of the Einstein ring. The analysis systematically explores the impact of physical parameters and observer position on the ring's morphology. As the observer's position varies, the image transitions from a complete ring to an arc and eventually to a single bright point. The Einstein ring radius is observed to decrease with increasing radial source position $\rho$, wave frequency $\omega$, and chemical potential $\mu$, while it increases with electric charge $e$ and temperature $T$. In contrast, the quantum correction parameter $a$ has negligible effect on the ring radius or response amplitude, as its contribution falls off rapidly near the boundary and remains subleading in the wave dynamics. The parameter $e$ enhances the electromagnetic lensing strength, leading to a broader ring, whereas increasing $\rho$ alters wavefront propagation, affecting both brightness peak and ring location. Geometric optics analysis confirms that the incident angle of the photon ring matches the Einstein ring angle, validating consistency across frameworks. Overall, the results highlight how nonlinear electromagnetic effects and bulk field configurations manifest in observable boundary features, providing a means to distinguish quantum-corrected black holes from classical solutions.