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We obtain (2+1) dimensional p-wave holographic superconductors from charged Born-Infeld black holes in the presence of massive charged vector fields in a bulk $AdS_4$ Einstein-Born-Infeld theory through the $AdS_4$-$CFT_3$ correspondence. Below a certain critical transition temperature the charged black hole develops vector hair that corresponds to charged vector condensate in the strongly coupled (2+1) dimensional boundary field theory that breaks both the $U(1)$ symmetry as well as the rotational invariance. The holographic free energy is computed for the boundary field theory which shows that the vector order parameter exhibits a rich phase structure involving zeroth order, first order, second order and retrograde phase transitions for different values of the backreaction and the Born-Infeld parameters. We numerically compute the ac conductivity for the p-wave superconducting phase of the strongly coupled (2+1) dimensional boundary field theory which also depends on the relative values of the parameters in the theory.
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We study the effects of the Born-Infeld electrodynamics on the holographic superconductors in the background of a Schwarzschild AdS black hole spacetime. We find that the presence of Born-Infeld scale parameter decreases the critical temperature and the ratio of the gap frequency in conductivity to the critical temperature for the condensates. Our results means that it is harder for the scalar condensation to form in the Born-Infeld electrodynamics.
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.
We numerically investigate the evolution of the holographic subregion complexity during a quench process in Einstein-Born-Infeld theory. Based on the subregion CV conjecture, we argue that the subregion complexity can be treated as a probe to explore the interior of the black hole. The effects of the nonlinear parameter and the charge on the evolution of the holographic subregion complexity are also investigated. When the charge is sufficiently large, it not only changes the evolution pattern of the subregion complexity, but also washes out the second stage featured by linear growth.
The requirement of the existence of a holographic c-function for higher derivative theories is a very restrictive one and hence most theories do not possess this property. Here, we show that, when some of the parameters are fixed, the $Dgeq3$ Born-Infeld gravity theories admit a holographic c-function. We work out the details of the $D=3$ theory with no free parameters, which is a non-minimal Born-Infeld type extension of new massive gravity. Moreover, we show that these theories generate an infinite number of higher derivative models admitting a c-function in a suitable expansion and therefore they can be studied at any truncated order.
The phenomenon of spontaneous scalarization of Reissner-Nordstr{o}m (RN) black holes has recently been found in an Einstein-Maxwell-scalar (EMS) model due to a non-minimal coupling between the scalar and Maxwell fields. Non-linear electrodynamics, e.g., Born-Infeld (BI) electrodynamics, generalizes Maxwells theory in the strong field regime. Non-minimally coupling the BI field to the scalar field, we study spontaneous scalarization of an Einstein-Born-Infeld-scalar (EBIS) model in this paper. It shows that there are two types of scalarized black hole solutions, i.e., scalarized RN-like and Schwarzschild-like solutions. Although the behavior of scalarized RN-like solutions in the EBIS model is quite similar to that of scalarize solutions in the EMS model, we find that there exist significant differences between scalarized Schwarzschild-like solutions in the EBIS model and scalarized solutions in the EMS model. In particular, the domain of existence of scalarized Schwarzschild-like solutions possesses a certain region, which is composed of two branches. The branch of larger horizon area is a family of disconnected scalarized solutions, which do not bifurcate from scalar-free black holes. However, the branch of smaller horizon area may or may not bifurcate from scalar-free black holes depending on the parameters. Additionally, these two branches of scalarized solutions can be both entropically disfavored over comparable scalar-free black holes in some parameter region.
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