Hydro-elastic complementarity in black branes at large D

We obtain the effective theory for the non-linear dynamics of black branes — both neutral and charged, in asymptotically flat or anti-desitter spacetimes — to leading order in the inverse-dimensional expansion. we find that black branes evolve as viscous fluids, but when they settle down they are more naturally viewed as solutions of an elastic soap-bubble theory. the two views are complementary: the same variable is regarded in one case as the energy density of the fluid, in the other as the deformation of the elastic membrane. the large-d theory captures finite-wavelength phenomena beyond the conventional reach of hydrodynamics. for asymptotically flat charged black branes (either reissner-nordstrom or p-brane-charged black branes) it yields the non-linear evolution of the gregory-laflamme instability at large d and its endpoint at stable non-uniform black branes. for reissner-nordstrom ads black branes we find that sound perturbations do not propagate (have purely imaginary frequency) when their wavelength is below a certain charge-dependent value. we also study the polarization of black branes induced by an external electric field.