In the AdS/CFT description of four-dimensional QCD matter undergoing Bjorken expansion, does the holographic energy-momentum tensor contain a Casimir-type contribution that should not be attributed to thermal matter? When the bulk isometry ansatz tha
t yielded such a Casimir term for (1+1)-dimensional boundary matter is generalised to a four-dimensional boundary, we show that a Casimir term does not arise, owing to singularities in the five-dimensional bulk solution. The geometric reasons are traced to a difference between the isometries of AdS_3 and AdS_{d+1} for d>=3.
We study the AdS/CFT thermodynamics of the spatially isotropic counterpart of the Bjorken similarity flow in d-dimensional Minkowski space with d>=3, and of its generalisation to linearly expanding d-dimensional Friedmann-Robertson-Walker cosmologies
with arbitrary values of the spatial curvature parameter k. The bulk solution is a nonstatic foliation of the generalised Schwarzschild-AdS black hole with a horizon of constant curvature k. The boundary matter is an expanding perfect fluid that satisfies the first law of thermodynamics for all values of the temperature and the spatial curvature, but it admits a description as a scale-invariant fluid in local thermal equilibrium only when the inverse Hawking temperature is negligible compared with the spatial curvature length scale. A Casimir-type term in the holographic energy-momentum tensor is identified from the threshold of black hole formation and is shown to take different forms for k>=0 and k<0.
We find the three-dimensional gravity dual of a process in which two clouds of (1+1)-dimensional conformal matter moving in opposite directions collide. This gives the most general conformally invariant holographic flow in the 1+1 dimensional boundar
y theory in terms of two arbitrary functions. With a suitable choice of the arbitrary functions the process can be interpreted as an opaque collision of two extended systems with central, fragmentation and interaction regions. Comparison with classical gluon field calculations relates the size of the system with the saturation scale.
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 ar
e 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.
