https://doi.org/10.1140/epjc/s10052-024-12522-1
Regular Article - Theoretical Physics
Holographic Einstein rings of non-commutative black holes
1
College of Economic and Management, Chongqing Jiaotong University, 400074, Chongqing, China
2
Department of Mechanics, Chongqing Jiaotong University, 400074, Chongqing, China
3
Center for Gravitational Wave Experiment, National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, 100190, Beijing, China
4
Lanzhou Center of Theoretical Physics, Lanzhou University, No. 222 South Tianshui Road, 730000, Lanzhou, China
Received:
2
January
2024
Accepted:
2
February
2024
Published online:
27
February
2024
With the help of AdS/CFT correspondence, we derive the desired response function of QFT on the boundary of the non-commutative black hole. Using the virtual optical system with a convex lens, we obtain the Einstein rings of the black hole from the response function. All the results show that the holographic ring always appears with the concentric stripe when the observer located at the north pole. With the change of the observation position, the ring changes into a luminosity-deformed ring, or bright spot. We also investigate the effect of the non-commutative parameter on the ring and find the ring radius becomes larger as the parameter increases. The effect of the temperature on the ring radius is also investigated, it is found that the higher the temperature, the smaller the ring radius. In addition, we also obtain the ingoing angle of the photon via geometric optics, as expected, this angle is consistent well with the angle of the Einstein ring obtained via holography.
© The Author(s) 2024
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