Holographic Einstein rings of Non-commutative black holes

TL;DR

This paper uses the AdS/CFT correspondence and optical system analogies to analyze the Einstein rings of non-commutative black holes, revealing how their features depend on temperature and non-commutative parameters.

Contribution

It introduces a novel method combining holography and optical analogies to study Einstein rings in non-commutative black holes, highlighting unique features due to non-commutativity.

Findings

Einstein ring features vary with observation position and non-commutative parameters.

The response function and ring brightness depend on temperature and non-commutative parameter.

Distinct behaviors in the response function can distinguish different black hole backgrounds.

Abstract

With the help of the AdS/CFT correspondence, we easily derive the desired response function of QFT on the boundary. Using the virtual optical system with a convex lens, we are able to obtain the image of the black hole from the response function and further study the Einstein ring of the non-commutative black holes. All the results show that there are some common features and different features compared to the previous study of other background black holes. And with the change of the observation position, this ring will change into a luminosity-deformed ring, or light points. In addition to these similarities, there are some different features which are due to the singularity of the event horizon temperature. Explicitly, the relation between temperature and the event horizon $T-z_h$ has two branches when the non-commutative parameter $n$ is fixed. These in turn have an effect on the behavior of the response function and the Einstein ring. However, the amplitude of $|\langle O\rangle|$ increases with the decrease of the temperature $T$ for the left branch of $T-z_h$ relation, while the amplitude of $|\langle O\rangle|$ decreases with the decrease of the temperature $T$ for the right branch. These differences are also reflected in the Einstein ring. Therefore, these differences can be used to distinguish different black hole backgrounds. Furthermore, we show that the non-commutative parameter has an effect on the brightness and the position of Einstein ring.