Relativistic Holographic Hydrodynamics from Black Hole Horizons

Understand

We consider the AdS/CFT correspondence in the hydrodynamic regime up to the second order in a derivative expansion.

• We demonstrate that the fluid conservation equations are equivalent to Einstein's constraint equations projected on different hyper-surfaces.
• We derive that result for hyper-surfaces of the form r=R(x) up to the first order in a derivative expansion of the metric.
• At the second order expansion, we introduce the notion of different black hole horizons, and focus on two particular horizon hyper-surfaces: the event horizon and the apparent horizon.