Holographic Fluids from 5D Dilaton Gravity

We study a solvable class of five-dimensional dilaton gravity models that continuously interpolate between anti-de Sitter (AdS$_5$), linear dilaton (LD$_5$) and positively curved spacetimes as a function of a continuous parameter $\nu$. The dilaton vacuum expectation value is set by a potential localized on a flat brane. We chart the elementary properties of these backgrounds for any admissible $\nu$, and determine stability conditions of the brane-dilaton system. We find that the spectrum of metric fluctuations can be either continuous or discrete. It features a massless graviton mode confined between the brane and the curvature singularity, and a massive radion mode tied to brane-dilaton stability. We show that, in the presence of a bulk black hole, the holographic theory living on the brane features a perfect fluid. The equation of state of the holographic fluid interpolates between radiation, pressureless matter and vacuum energy as a function of $\nu$. This extends earlier findings on holographic fluids. Our results suggest that the thermodynamics of the fluid mirrors precisely the thermodynamics of the bulk black hole.