Holographic Einstein rings of non-commutative black holes

Abstract 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.