Holographic Einstein ring of a charged Rastall AdS black hole with bulk electromagnetic field*

Abstract

We study the Einstein images of a charged Rastall AdS black hole (BH)
within the fabric of AdS/CFT correspondence. Considering the holographic setup,
we analyze the amplitude of the total response function for various values of
model parameters. With an increase in parameter $\lambda$ and temperature $T$,
the amplitude of the response function is decreased, while it is increased with
the increase of the electric charge $e$ and chemical potential $\mu$.
The influence of frequency $\omega$ also plays an important role in
the bulk field, as it is found that the decreasing $\omega$ leads to
an increase in the periods of the waves, which means that the amplitude
of the response function also depends on the wave source. The relation
between $T$ to the inverse of the horizon $r_{h}$ for the parameter $\lambda$ is
interpreted under fixed values of other involved parameters. These, in turn,
affect the behavior of the response function and the Einstein ring, which may
be used to differentiate the present work from previous studies. Via a special
optical system, we construct the holographic images of the BH in bulk. These
results show that the Einstein ring always appears with concentric stripes at
the position of the north pole, and this ring transforms into the luminosity-deformed
ring or bright light spot when the distant observer lies away from the north pole.
Finally, we finish this work with a discussion of the influence of the associated
parameters on the Einstein ring radius, which is consistent with wave optics.