From quasinormal modes of rotating black strings to hydrodynamics of a moving CFT plasma

Abstract

A certain identification of points in a planar Schwarzschild-anti de Sitter (AdS) black hole generates a four-dimensional static black string. In turn, a rotating black string can be obtained from a static one by means of a local boost along the compact direction. On the basis of the gauge/gravity duality, these black strings are dual to rotating thermal states of a strongly interacting conformal field theory (CFT) that lives on a cylinder. In this work, we obtain the complete quasinormal mode (QNM) spectrum of the gravitational perturbations of rotating black strings. Analytic solutions for the dispersion relations are found in the hydrodynamic limit, characterized by fluctuations with wavenumber and frequency much smaller than the Hawking temperature of the string (or the temperature of the CFT in the dual description). We obtain these dispersion relations both by studying the gravitational perturbations of rotating black strings and by investigating relativistic wave vectors in a moving fluid living on the boundary of the AdS spacetime. Relativistic effects like the Doppler shift of the frequencies, wavelength contraction, and dilation of the thermalization time are shown explicitly in such a regime. The numerical solutions for the fundamental QNMs show a crossover (a transition) from a hydrodynamic-like behavior to a linear relativistic scaling for large wavenumbers. Additionally, we find a new family of QNMs which are purely damped in the zero wavenumber limit and that does not follow as a continuation of QNMs of the static black string, but that appears to be closely related to the algebraically special perturbation modes. I. INTRODUCTIONSince its advent in the late 1990's, the celebrated antide Sitter/conformal field theory (AdS/CFT) correspondence [1-4] has been extended and applied to different areas of physics. Such developments have lead to what is now known as the AdS/QCD [5][6][7][8], the AdS/condensed matter [9][10][11], and the fluid/gravity [12][13][14] correspondences. Over the last two decades, the AdS/CFT duality has allowed the study of properties of strongly coupled systems in a n-dimensional flat spacetime by mapping them to a weakly coupled gravitational theory in an asymptotically AdS n+1 spacetime. In applications to particle physics, top-down and bottom-up models were used to study, among other things, the mass spectrum, the correlation functions, and the deep inelastic scattering of glueballs, vector and scalar mesons [15][16][17][18][19][20][21][22][23]. Some phenomena in condensed matter, such as the hightemperature superconductivity [24][25][26], the classical and quantum Hall effects [27][28][29][30][31][32] and the (non-)Fermi liquid behavior of certain materials [33][34][35], were also object of study in the literature. In relation to plasma physics, the fluid/gravity correspondence establishes a one-to-one

Hydrodynamics of simply spinning black holes & hydrodynamics for spinning quantum fluids

“…We have demonstrated validity of these relations by explicit calculation in our holographic model. Equation (5.9) is further verified by comparison to the hydrodynamic sound and shear diffusion modes found in AdS 4 rotating black strings [42]. Recall, that in the latter work, the authors consider a spacetime which has the topology of a cylinder but is locally a boosted black brane.…”

“…Rotating black holes have been considered in the context of the AdS/CFT correspondence before, pioneered by [11,12]. QNM frequencies of rotating (charged) AdS 4 black strings were computed, and the hydrodynamic modes of the dual two-dimensional field theory were discussed [40][41][42]. Apart from the spacetime dimension, this setup differs from ours in that its topology is cylindrical and is locally a boosted black brane.…”

“…Apart from the spacetime dimension, this setup differs from ours in that its topology is cylindrical and is locally a boosted black brane. 5 While our perturbations (except for limiting cases) carry angular momentum, the perturbations in [42] propagate with linear momentum. However, we can still compare the general form of the hydrodynamic shear diffusion and sound dispersion relations, to our results and to [26,27].…”

Quasinormal modes and dispersion relations for quarkonium in a plasma

“…Previous studies of quasinormal modes in the context of gauge/gravity duality can be found, for example, in Refs. [14][15][16][17][18][19][20][21][22][23][24][25]. It is interesting to note that when one considers the conformal holographic AdS/CFT case, like in refs.…”

Thermal dissociation of heavy mesons and configurational entropy

“…Previous studies of quasinormal modes in the context of gauge/gravity duality can be found, for example, in Refs. [32][33][34][35][36][37][38][39][40][41][42]. Quasinormal modes are obtained solving the equation that comes from the metric (11):…”