Dissipative Bjorken hydrodynamics from an AdS Schwarzschild black hole

TL;DR

This paper derives dissipative Bjorken hydrodynamics from a higher-dimensional Schwarzschild black hole using holography, calculating the metric and stress-energy tensor to high order and confirming the viscosity-to-entropy ratio.

Contribution

It provides a detailed holographic derivation of time-dependent dissipative hydrodynamics from an AdS black hole, including higher-order corrections and boost invariance perturbations.

Findings

Confirmed the viscosity-to-entropy ratio of 1/4π in a time-dependent setting

Calculated the Schwarzschild metric to next-to-next-to-leading order in large τ expansion

Aligned results with known five-dimensional Einstein equation solutions

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 $\tau$. Using an appropriate slicing near the boundary, we calculate the Schwarzschild metric to next-to-next-to-leading order in the large $\tau$ 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, $1/(4\pi)$, 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.