Forced Fluid Dynamics from Blackfolds in General Supergravity Backgrounds

We present a general treatment of the leading order dynamics of the collective modes of charged dilatonic $p$-brane solutions of (super)gravity theories in arbitrary backgrounds. To this end we employ the general strategy of the blackfold approach which is based on a long-wavelength derivative expansion around an exact or approximate solution of the (super)gravity equations of motion. The resulting collective mode equations are formulated as forced hydrodynamic equations on dynamically embedded hypersurfaces. We derive them in full generality (including all possible asymptotic fluxes and dilaton profiles) in a far-zone analysis of the (super)gravity equations and in representative examples in a near-zone analysis. An independent treatment based on the study of external couplings in hydrostatic partition functions is also presented. Special emphasis is given to the forced collective mode equations that arise in type IIA/B and eleven-dimensional supergravities, where besides the standard Lorentz force couplings our analysis reveals additional couplings to the background, including terms that arise from Chern-Simons interactions. We also present a general overview of the blackfold approach and some of the key conceptual issues that arise when applied to arbitrary backgrounds.