Abstract
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.
Highlights
A model of the holographic superconductor on S2 is composed of a Maxwell field and charged scalar field in a fixed spherical AdS black hole background [12,13,14]. (We only focus on the probe limit of the holographic superconductor.) When the Hawking temperature is smaller than a critical temperature T < Tc, the AdS black hole becomes unstable against charged scalar field perturbation
We proposed a way to take the image of the black hole that is dual to a superconductor
We considered an external time-periodic localized electromagnetic field in the superconductor and its response
Summary
We consider the s-wave holographic superconductor without the back reaction from the gravity [13]. Consider the following Einstein-Maxwell-charged scalar system, of which Lagrangian density is. Where G, R, L, Fμν, Dμ, Ψ are the gravitational constant, the Ricci scalar, the AdS radius, the field strength, the covariant derivative with respect to the background metric and the U(1) gauge field, and the charged scalar field, respectively. We will consider the scalar field and the U(1) gauge field as the probe fields. This is achieved by taking G → 0. [23] for the back reacted case.) we can choose the Sch-AdS4 (2.1) as the background spacetime solution.. The charged scalar field Ψ and the U(1) gauge field Aμ follows the equations below. We will solve these equations of motion
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