Holographic images of an AdS black hole within the framework of <inline-formula><math xmlns:mml=

doi:10.1007/s11467-024-1393-8

Front. Phys.

2024, Vol. 19

Issue (5) : 54202 https://doi.org/10.1007/s11467-024-1393-8

Holographic images of an AdS black hole within the framework of

f (R)

gravity theory

Guo-Ping Li¹(

), Ke-Jian He², Xin-Yun Hu³, Qing-Quan Jiang¹(

)

¹. School of Physics and Astronomy, China West Normal University, Nanchong 637000, China
². College Of Physics, Chongqing University, Chongqing 401331, China
³. College of Economic and Management, Chongqing Jiaotong University, Chongqing 400074, China

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Abstract

Based on the AdS/CFT correspondence, this study employs an oscillating Gaussian source to numerically study the holographic images of an AdS black hole under $f (R)$ gravity using wave optics. Due to the diffraction of scalar wave, it turns out that one can clearly observed the interference patten of the absolute amplitude of response function on the AdS boundary. Furthermore, it is observed that its peak increases with the $f (R)$ parameter $α$ but decreases with the global monopole $η$ , frequency $ω$ , and horizon $r h$ . More importantly, the results reveal that the holographic Einstein ring is a series of concentric striped patterns for an observer at the North Pole and that their center is analogous to a Poisson–Arago spot. This ring can evolve into a luminosity-deformed ring or two light spots when the observer is at a different position. According to geometrical optics, it is true that the size of the brightest holographic ring is approximately equal to that of the photon sphere, and the two light spots correspond to clockwise and anticlockwise light rays. In addition, holographic images for different values of black holes and optical system parameters were obtained, and different features emerged. Finally, we conclude that the holographic rings of the AdS black hole in modified gravities are more suitable and helpful for testing the existence of a gravity dual for a given material.

Keywords AdS black hole holographic images AdS/CFT correspondence

Corresponding Author(s): Guo-Ping Li,Qing-Quan Jiang

Issue Date: 22 May 2024

Cite this article:

Guo-Ping Li,Ke-Jian He,Xin-Yun Hu, et al. Holographic images of an AdS black hole within the framework of

f (R)

gravity theory[J]. Front. Phys. , 2024, 19(5): 54202.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-024-1393-8
https://academic.hep.com.cn/fop/EN/Y2024/V19/I5/54202

Fig.1 Schematic of the imaging of a dual black hole.

Fig.2 Detailed transformation of the response function

? O ?

on the screen.

Fig.3 Amplitude of

| ? O ? |

around the North Pole.

Fig.4 The holographic images for

ψ 0 = 0.1, η = 0.25, ω = 75, r h = 0.75, d = 0.6, σ = 0.05

, where the vertical line reads

y s / f

and horizontal axis is

x s / f

, and their range belongs to

(− 1.3, 1.3)

, which also used in later similar figures.

Fig.5 Holographic images for

d = 0.6, σ = 0.05, ω = 75

Fig.6 Holographic images for

ψ 0 = 0.25, η = 0.1, r h = 0.75

Fig.7 Effective potential and photon orbit.

Fig.8 Angle

θ h r

in Eq. (28).

Fig.9 Radius of the photon sphere and holographic Einstein ring.

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