Holographic Einstein Ring of Quantum Corrected AdS-Reissner-Nordstrom Black Holes in Kiselev Spacetime

TL;DR

This paper investigates the holographic Einstein ring of quantum-corrected AdS-Reissner-Nordstrom black holes in Kiselev spacetime using wave optics and AdS/CFT correspondence, analyzing how physical parameters influence the ring's characteristics.

Contribution

It introduces a holographic imaging method for Einstein rings in quantum-corrected black holes within Kiselev spacetime, combining wave optics with holography in AdS/CFT context.

Findings

Ring transitions from axisymmetric to arc with observer position

Ring radius decreases with quantum correction, temperature, chemical potential

Ring radius increases with cosmological fluid parameter and wave frequency

Abstract

This study, grounded in AdS/CFT correspondence, utilizes wave optics theory to explore the Einstein ring of a quantum-corrected AdS-Reissner-Nordstr\"om black hole (BH) in Kiselev spacetime. By fixing the wave source on the AdS boundary, the corresponding response function generated on the antipodal side of the boundary is successfully obtained. Using a virtual optical system with a convex lens, the holographic image of the Einstein ring of the BH is captured on a screen. The study also investigates the impact of various physical parameters and the observer's position on the characteristics of the Einstein ring. The results indicate that changes in the observer's position cause the image to transition from an axisymmetric ring to an arc, ultimately converging to a single luminous point. Additionally, the Einstein ring radius decreases with increasing values of the quantum correction parameter $a$, the equation of state parameter $\Omega$, temperature $T$, and chemical potential $\mu$ , respectively. In contrast, the ring radius increases as the cosmological fluid parameter $c$ increases. Furthermore, the ring radius becomes more distinct as the wave source frequency $\omega$ increases. From the perspective of geometric optics, the photon ring of the quantum-corrected AdS-Reissner-Nordstr\"om BH in Kiselev spacetime is further studied. Numerical results suggest that the incident angle of the photon ring aligns with that of the Einstein ring.