A Holographic Dual of Bjorken Flow

TL;DR

The paper constructs a time-dependent holographic dual for Bjorken flow in ${ m N}=4$ SYM using ingoing EF coordinates and a late-time $ au^{-2/3}$ expansion. By solving the 5d Einstein equations order by order and enforcing bulk regularity, the authors show that the shear viscosity and certain second-order transport coefficients are uniquely fixed, and that the bulk geometry remains regular (except at the origin) when these coefficients are chosen appropriately. They prove the existence of an apparent horizon, hence an event horizon, rendering the dual geometry a dynamical black hole and providing a concrete time-dependent AdS/CFT example. The work also explains why previous FG-coordinate approaches fail to capture horizon structure and highlights a link between horizon regularity and hydrodynamic data, with implications for entropy and non-staticity in the holographic plasma.

Abstract

We propose a consistent setup for a holographic dual of Bjorken flow of strongly coupled large-Nc N=4 SYM-theory plasma. We employ Eddington-Finkelstein type coordinates for the dual geometry, and we propose a late-time expansion there. We construct the dual geometry order by order, and we show that the transport coefficients are determined by the regularity of the geometry. We also show that the dual geometry has an apparent horizon hence an event horizon, which covers the singularity at the origin. We prove that the dual geometry is regular at all orders under an appropriate choice of the transport coefficients. Our model is a concrete well-defined example of time-dependent AdS/CFT.