Close encounters with attractors of the third kind

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.