Dissipative Bjorken hydrodynamics from an AdS Schwarzschild black hole
Abstract
We discuss the derivation of dissipative Bjorken hydrodynamics from a Schwarzschild black hole in asymptotically AdS spacetime of arbitrary dimension in the limit of large longitudinal proper time τ. Using an appropriate slicing near the boundary, we calculate the Schwarzschild metric to next-to-next-to-leading order in the large τ expansion as well as the dual stress-energy tensor on the boundary via holographic renormalization. At next-to-next-to-leading order, it is necessary to perturb the Schwarzschild metric in order to maintain boost invariance. The perturbation has a power law time dependence and leads to the same value of the ratio of viscosity to entropy density, 1/(4π), as in the case of sinusoidal perturbations. Our results are in agreement with known time-dependent asymptotic solutions of the Einstein equations in five dimensions.