On analytical study of holographic superconductors with Born–Infeld electrodynamics

Based on the Sturm–Liouville eigenvalue problem, Banerjee et al. proposed a perturbative approach to analytically investigate the properties of the ( 2+1 )-dimensional superconductor with Born–Infeld electrodynamics (Banerjee et al., 2013) [29] . By introducing an iterative procedure, we will further improve the analytical results and the consistency with the numerical findings, and can easily extend the analytical study to the higher-dimensional superconductor with Born–Infeld electrodynamics. We observe that the higher Born–Infeld corrections make it harder for the condensation to form but do not affect the critical phenomena of the system. Our analytical results can be used to back up the numerical computations for the holographic superconductors with various condensates in Born–Infeld electrodynamics

Notes on analytical study of holographic superconductors with Lifshitz scaling in external magnetic field

We employ the matching method to analytically investigate the holographic superconductors with Lifshitz scaling in an external magnetic field. We discuss systematically the restricted conditions for the matching method and find that this analytic method is not always powerful to explore the effect of external magnetic field on the holographic superconductors unless the matching point is chosen in an appropriate range and the dynamical exponent z satisfies the relation <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>d</mi><mo>−</mo><mn>1</mn></math> or <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>d</mi><mo>−</mo><mn>2</mn></math> . From the analytic treatment, we observe that Lifshitz scaling can hinder the condensation to be formed, which can be used to back up the numerical results. Moreover, we study the effect of Lifshitz scaling on the upper critical magnetic field and reproduce the well-known relation obtained from Ginzburg–Landau theory

Strong gravitational lensing in a rotating Kaluza-Klein black hole with squashed horizons

We have investigated the strong gravitational lensing in a rotating squashed Kaluza-Klein (KK) black hole spacetime. Our result show that the strong gravitational lensings in the rotating squashed KK black hole spacetime have some distinct behaviors from those in the backgrounds of the four-dimensional Kerr black hole and of the squashed KK Gödel black hole. In the rotating squashed KK black hole spacetime, the marginally circular photon radius ρ ps , the coefficient $\overline{a}$ , $\overline{b}$ , the deflection angle α ( θ ) in the ϕ direction and the corresponding observational variables are independent of whether the photon goes with or against the rotation of the background, which is different with those in the usual four-dimensional Kerr black hole spacetime. Moreover, we also find that with the increase of the scale of extra dimension ρ 0 , the marginally circular photon radius ρ ps and the angular position of the relativistic images θ ∞ first decreases and then increases in the rotating squashed KK black hole for fixed rotation parameter b , but in the squashed KK Gödel black hole they increase for the smaller global rotation parameter j and decrease for the larger one. In the extremely squashed case ρ 0 = 0, the coefficient a in the rotating squashed KK black hole increases monotonously with the rotation parameter, but in the squashed KK Gödel black hole it is a constant and independent of the global rotation of the Gödel Universe. These information could help us to understand further the effects of the rotation parameter and the scale of extra dimension on the strong gravitational lensing in the black hole spacetimes