Close encounters with attractors of the third kind

TL;DR

This paper identifies a hydrodynamic attractor in a novel hyperbolic geometry within the Mueller-Israel-Stewart framework, revealing rapid approach to hydrodynamics despite high Knudsen numbers, with implications for fluid behavior in curved spacetime.

Contribution

It extends the understanding of hydrodynamic attractors to a new hyperbolic geometry, showing rapid hydrodynamization even when traditional parameters suggest non-hydrodynamic behavior.

Findings

Hydrodynamic attractor exists in the new geometry.

Fluid behaves like a localized droplet propagating along the lightcone.

Hydrodynamization occurs rapidly despite high Knudsen number.

Abstract

We report on the existence of a hydrodynamic attractor in the Mueller-Israel-Stewart framework of a fluid living in the novel geometry discovered recently by Grozdanov. This geometry, corresponding to a hyperbolic slicing of dS$_3\times\mathbb{R}$, complements previous analyses of attractors in Bjorken (flat slicing) and Gubser (spherical slicing) flows. The fluid behaves like a sharply localized droplet propagating rapidly along the lightcone. Typical solutions approach the hydrodynamic attractor rapidly at late times despite a Knudsen number exceeding unity, suggesting that the inverse Reynolds number captures hydrodynamization more faithfully since the shear stress vanishes at late times. This is in stark contrast to Gubser flow, which has both the Knudsen and inverse Reynolds number becoming small for intermediate times. We close with a comparison to Weyl-transformed Bjorken flow and discuss possible phenomenological applications.