Black brane entropy and hydrodynamics: the boost-invariant case

TL;DR

This paper extends the framework of slowly evolving horizons to black branes in AdS spaces, analyzing horizon behavior in boost-invariant flow and addressing entropy ambiguity in fluid/gravity duality.

Contribution

It generalizes the slowly evolving horizons framework to black branes in AdS and explores entropy ambiguity in boost-invariant hydrodynamics within the gravity dual.

Findings

Identifies entropy ambiguity at second order in gradient expansion.

Links gravity-side freedom to hydrodynamic entropy current ambiguity.

Provides a phenomenological approach to black brane entropy in time-dependent scenarios.

Abstract

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.