Abstract
Using AdS/CFT correspondence, we analyze the holographic Einstein images via the response function of the complex scalar field as a probe wave on an AdS Schwarzschild scalar-tensor-vector gravity (STVG) black hole (BH). We find that the amplitude of the response function decreases with increasing values of coupling parameter α and increases with decreasing temperature T. The frequency ω of the wave source also plays a significant role in wave periods; as we increase the values of ω, the periods of waves decrease, indicating that the total response function closely depends on the wave source. Further, we investigate the optical appearance of the holographic images of the BH in bulk. We found that the holographic ring always appears with surrounding concentric stripes when the observer is located at the north pole, and an extremely bright ring appears when the observer is at the position of the photon sphere of the BH. This ring changes into a luminosity-deformed ring or a bright light spot as the observational angle changes. The corresponding brightness profiles show that the luminosity of the ring decreases and the shadow radius increases with increasing values of α. The relation between temperature T and the inverse of the horizon is discussed; T is small at the beginning of the horizon and then increases as the horizon radius increases. This effect can be used to distinguish the STVG BH solution from other BH solutions. Moreover, these significant features are also reflected in the Einstein ring and corresponding brightness profiles. In addition, we compare the results obtained by wave optics and geometric optics, which align well, implying that the holographic scheme adopted in this study is valid.
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