Near-extremal fluid mechanics

A bstract We analyse near-extremal black brane configurations in asymptotically AdS 4 spacetime with the temperature T , chemical potential μ and three-velocity u ν varying slowly. consider a low-temperature limit where rate of variation is much slower than but bigger . This different from one considered for conventional fluid-mechanics which smaller both find that our limit, as well, Einstein-Maxwell equations can be solved systematic perturbative expansion. At first order, variation, resulting constitutive relations stress tensor charge current are local boundary theory easily calculated. higher orders, we show these become non-local time expansion still valid. there four linearised modes this limit; similar to hydrodynamic found fluid mechanics same dispersion relations. also study some independent perturbations exhibiting attractor behaviour at horizon — arise presence external driving forces theory.