Black brane entropy and hydrodynamics: The boost-invariant case

The framework of slowly evolving horizons is generalized to the case of black branes in asymptotically anti–de Sitter spaces in arbitrary dimensions. The results are used to analyze the behavior of both event and apparent horizons in the gravity dual to boost-invariant flow. These considerations are motivated by the fact that at second order in the gradient expansion the hydrodynamic entropy current in the dual Yang-Mills theory appears to contain an ambiguity. This ambiguity, in the case of boost-invariant flow, is linked with a similar freedom on the gravity side. This leads to a phenomenological definition of the entropy of black branes. Some insights on fluid/gravity duality and the definition of entropy in a time-dependent setting are elucidated.