Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics

TL;DR

This paper derives an analytical solution for viscous relativistic hydrodynamics in a Bjorken flow, identifies the hydrodynamic attractor, and reveals the divergence of the slow-roll expansion, challenging its common use.

Contribution

It provides the first analytical solution for the hydrodynamic attractor in this context and demonstrates the divergence of the slow-roll expansion.

Findings

Hydrodynamic attractor analytically determined

Slow-roll expansion diverges in this setting

Gradient expansion converges despite causality issues

Abstract

We find the general analytical solution of the viscous relativistic hydrodynamic equations (in the absence of bulk viscosity and chemical potential) for a Bjorken expanding fluid with a constant shear viscosity relaxation time. We analytically determine the hydrodynamic attractor of this fluid and discuss its properties. We show for the first time that the slow-roll expansion, a commonly used approach to characterize the attractor, diverges. This is shown to hold also in a conformal plasma. The gradient expansion is found to converge in an example where causality and stability are violated.