Electromagnetic quasinormal modes of rotating black strings and the AdS/CFT correspondence

Abstract

We investigate the quasinormal spectrum of electromagnetic perturbations of rotating black strings. Among the solutions of Einstein equations in the presence of a negative cosmological constant there are asymptotically anti-de Sitter (AdS) black holes whose horizons have the topology of a cylinder. The stationary version of these AdS black holes represents rotating black strings. The conformal field theory (CFT) dual of a black string lives in a Minkowski space with a compact dimension. On the basis of the AdS/CFT duality, we interpret a CFT plasma moving with respect to the preferred rest frame introduced by the topology as the holographic dual to a rotating black string. We explore the consequences of this correspondence by investigating the electromagnetic perturbations of a black string for different rotation parameter values. As usual the electromagnetic quasinormal modes (QNM) correspond to the poles of retarded Green's functions of $R$-symmetry currents in the boundary field theory. The hydrodynamic regime of the QNM dispersion relations are analytically studied. Finally, we investigate numerically the effect of rotation on all the family of black-string electromagnetic quasinormal modes. We interpret these results from the CFT perspective and notice the emergence of effects like Doppler shift of the frequencies and dilation of the thermalization times.