Hydrodynamic attractors for the speed of sound in holographic Bjorken flow

TL;DR

This paper investigates the evolution of the speed of sound in a far-from-equilibrium holographic model of Bjorken flow, revealing the existence of distinct hydrodynamic attractors for different directions and their relation to hydrodynamization.

Contribution

It introduces the concept of hydrodynamic attractors for the speed of sound in holographic Bjorken flow and demonstrates their existence and properties through Borel resummation.

Findings

Identification of separate attractors for longitudinal and transverse speed of sound.

Reaching an attractor does not require local thermal equilibrium.

Attractors are associated with hydrodynamization, not thermalization.

Abstract

The time evolution of the averaged energy momentum tensor as well as its variation with energy density are calculated in a far-from-equilibrium state of $\mathcal{N}=4$ SYM theory undergoing a Bjorken expansion. The calculation is carried out holographically where we consider a collection of trajectories of the energy density in the space of solutions by small changes to the initial conditions of the bulk spacetime. We argue that the proper interpretation of the variation of the diagonal energy momentum tensor components with respect to the energy density is that of a far-from-equilibrium speed of sound. We demonstrate remarkable agreement with a corresponding hydrodynamic prediction. We find by Borel resummation that the holographic system has one attractor for this speed of sound longitudinal, and another transverse to the direction of Bjorken expansion. Attractor times for various initial flow conditions show that reaching an attractor does not imply or require local thermal equilibrium. In the cases studied, reaching an attractor implies hydrodynamization (quantities evolve approximately according to hydrodynamics), justifying the name \emph{hydrodynamic attractor }