Probing holographic Einstein ring of charged AdS black hole with nonlinear electrodynamics field

Abstract This study investigates the visual characteristics of holographic Einstein rings of AdS black hole (BH) with nonlinear electrodynamics (NED) under a wave optics framework. A wave source is fixed on one side of AdS boundary, producing a response function on the other side, from which a virtual optical system with a convex lens reconstructs the holographic image of the Einstein ring. The constructed framework reveals the influence of model parameters and the observer’s inclinations on the characteristics of the Einstein ring. The results indicate that changes in the observer’s position cause the image to evolve from an axisymmetric ring into two arcs, which subsequently transform into two bright spots located on the left and right sides of the screen. Moreover, the Einstein ring radius is increased with the aid of NED parameter $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> , while the width of the ring decreases and becomes sharper as the value of the wave source $$\omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ω</mml:mi> </mml:math> increases. Subsequently, the radius of the Einstein ring is significantly increased with T , while it decreases with chemical potential $$\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math> . Finally, the numerical results indicate the incident angle of the photon ring is consistent with that of the wave optics.