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 ${\mathrm{AdS}}_{3}$ gravity. We find an exact bulk solution, show that this solution describes part of the spinless Ba\~nados-Teitelboim-Zanelli black hole with the angular dimension unwrapped, and use the thermodynamics of the Ba\~nados-Teitelboim-Zanelli 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.
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