Gravity/Fluid Correspondence and Its Application on Bulk Gravity with $U(1)$ Gauge Field

As the long wavelength limit of the AdS/CFT correspondence, the gravity/fluid correspondence has been shown to be a useful tool for extracting properties of the fluid on the boundary dual to the gravity in the bulk. In this paper, after briefly reviewing the algorithm of gravity/fluid correspondence, we discuss the results of its application on bulk gravity with a $U(1)$ gauge field. In the presence of a $U(1)$ gauge field, the dual fluid possesses more interesting properties such as its charge current. Furthermore, an external field $A_\mu^{ext}$ could affect the charge current, and the $U(1)$ Chern-Simons term also reinduces extra structures to the dual current giving anomalous transport coefficients.