Forced non-conformal relativistic fluid from the Chamblin-Reall gravity

The Chamblin-Reall gravity is a remarkable non-conformal platform for the fluid/gravity correspondence to achieve its maximum efficiency. When a probe scalar field that does not change the background metric is manually introduced into the action of the gravity side, an external scalar field will appear at the boundary, and the gradients of the external scalar field will act as a driving force exerting on the dual relativistic fluid. Thus the dynamics of the fluid will be affected in the way that the stress tensor is no longer conserved. We will use the fluid/gravity correspondence to derive the transport coefficients related to the external scalar field and the explicit expression of the driving force.