Observing black holes through superconductors

We propose a way to observe the photon ring of the asymptotically anti-de Sitter black hole dual to a superconductor on the two-dimensional sphere. We consider the electric current of the superconductor under the localized time-periodic external electromagnetic field. On the gravity side, the bulk Maxwell field is sent from the AdS boundary and then diffracted by the black hole. We construct the image of the black hole from the asymptotic data of the bulk Maxwell field that corresponds to the electric current on the field theory side. We decompose the electric current into the dissipative and non-dissipative parts and take the dissipative part for the imaging of the black hole. We investigate the effect of the charged scalar condensate on the image. We obtain the bulk images that indicate the discontinuous change of the size of the photon ring.

Automated summary

The paper introduces a method to observe the photon ring of a superconductor dual to an asymptotically anti-de Sitter black hole on a two-dimensional sphere. By studying the relationship between the electric current and Maxwell field on both gravity and field theory sides, the dissipative part of the electric current is used for imaging the black hole, with results indicating that the charged scalar condensate affects the discontinuous changes in the size of the photon ring.