content_image/361962.jpg content_image/361963.jpg content_image/361964.jpg content_image/361965.jpg content_image/361966.jpg content_image/361967.jpg
described by 

<img src='content_image/361962.jpg'>

with deviations of less than 8%. This is roughly twice the BCS value 3.5 indicating that the holo- graphic superconductors are strongly coupled. However, the authors in Refs. [16, 42] found that this relation is not stable in the presence of the Gauss-Bonnet correction terms. And Cai et al. [36] got a relation 

<img src='content_image/361963.jpg'>

with the accuracy more than 93% for a planar Hoˇrava-Lifshit z black hole with the condition of the detailed balance. We now examine this result for the Hoˇrava -Lifshitz gravity considered here. 

In order to compute the electrical conductivity, we should study the electromagnetic perturbation in this Hoˇrava-Lifshitz black hole background, and then ca lculate the linear response to the perturba- tion. In the probe approximation, the e ff ect of the perturbation of metric can be ignored. Assuming that the perturbation of the vector potential is translational symmetric and has a time dependence as δ A$_{x}$ = A$_{x}$ ( r ) e − i ω $^{t}$, we find that the Maxwell equation in the Hoˇrava-Lifshitz bl ack hole background reads 

<img src='content_image/361964.jpg'>

where a prime denotes the derivative with respect to r . An ingoing wave boundary condition near the horizon is given by 

In the asymptotic AdS region ( r → ∞ ), the general behavior should be 

<img src='content_image/361965.jpg'>

<img src='content_image/361966.jpg'>

By using AdS / CFT correspondence and the Ohm’s law, we know that the conductivity can be ex- pressed as [8] 

<img src='content_image/361967.jpg'>

