Gravity dual of 1+1 dimensional Bjorken expansion

TL;DR

This paper applies AdS/CFT duality to model 1+1 dimensional Bjorken expansion, finding an exact bulk solution related to BTZ black holes, and describes the boundary fluid as an ideal gas in local thermal equilibrium.

Contribution

It provides an exact bulk solution in AdS_3 gravity for 1+1 dimensional Bjorken flow, linking it to BTZ black hole thermodynamics and extending the holographic description of heavy ion collisions.

Findings

Boundary fluid is an ideal gas in local thermal equilibrium.

Exact bulk solution describes part of a BTZ black hole with unwrapped angular dimension.

Including angular momentum yields boost-invariant flow with nonzero longitudinal velocity.

Abstract

We study the application of AdS/CFT duality to longitudinal boost invariant Bjorken expansion of QCD matter produced in ultrarelativistic heavy ion collisions. As the exact (1+4)-dimensional bulk solutions for the (1+3)-dimensional boundary theory are not known, we investigate in detail the (1+1)-dimensional boundary theory, where the bulk is AdS_3 gravity. We find an exact bulk solution, show that this solution describes part of the spinless Banados-Teitelboim-Zanelli (BTZ) black hole with the angular dimension unwrapped, and use the thermodynamics of the BTZ hole to recover the time-dependent temperature and entropy density on the boundary. After separating from the holographic energy-momentum tensor a vacuum contribution, given by the extremal black hole limit in the bulk, we find that the boundary fluid is an ideal gas in local thermal equilibrium. Including angular momentum in the bulk gives a boundary flow that is boost invariant but has a nonzero longitudinal velocity with respect to the Bjorken expansion.