Holographic Einstein Rings of anti-de Sitter Black Holes with Higher-Derivative Corrections in Presence of String Cloud

Abstract This paper seeks to explore the holographic optical appearance of an anti-de Sitter (AdS) black hole with higher-derivative corrections in the presence of a string cloud, drawing on the AdS/conformal field theory (CFT) correspondence and wave optics. We introduce a Gaussian wave source that oscillates at the AdS boundary and propagates through the bulk. The resulting response function is then analyzed using an imaging system to study the optical properties of the black hole. Depending on the observer’s position and variations in system parameters, the resulting holographic image takes on different forms, including a well-defined Einstein ring, deformed luminous patterns, or isolated bright spots. Notably, when the observer is positioned at the north pole, the image consistently features a bright ring at the photon sphere, encircled by concentric stripes. Our findings reveal a strong correlation between the Einstein ring’s location and the photon sphere radius predicted by geometric optics, reinforcing the connection between wave optics and gravitational lensing. Additionally, we examine the influence of higher-derivative corrections and string cloud parameters on the observed optical features.