Fluid Boundary Conditions from AdS/BCFT

In this paper, we initiate our program to classify conformal fluid boundary conditions, by utilizing the fluid/gravity correspondence in the AdS/BCFT correspondence. The AdS/BCFT correspondence is a conjectured duality between a quantum gravity in asymptotically AdS spacetime with an end-of-the world brane and a boundary conformal field theory (BCFT). We show that a choice of boundary condition for the metric on the end-of-the world brane naturally leads to specific boundary conditions for velocity field and temperature field of BCFT in the hydrodynamic limit. We analyze the Neumann, Dirichlet and Conformal boundary conditions for the metric on the end-of-the world brane, and discuss their implications for conformal fluid boundary conditions.