Kaluza-Klein reduction of relativistic fluids and their gravity duals
arXiv:1307.8365 · doi:10.1007/JHEP12(2013)087
Abstract
We study the hydrodynamics of relativistic fluids with several conserved global charges (i.e., several species of particles) by performing a Kaluza-Klein dimensional reduction of a neutral fluid on a N-torus. Via fluid/gravity correspondence, this allows us to describe the long-wavelength dynamics of black branes with several Kaluza-Klein charges. We obtain the equation of state and transport coefficients of the charged fluid directly from those of the higher-dimensional neutral fluid. We specialize these results for the fluids dual to Kaluza-Klein black branes.
v2, Important additions: (1) discussion of the first law for the reduced fluid, (2) transport coefficients in terms of the temperature and the chemical potentials. Some comments and references added. 24 pages
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