A family of three maximally symmetric boost-invariant flows in relativistic hydrodynamics

Abstract

I discuss the constructions of boost-invariant dissipative conformal hydrodynamic flows by elaborating on the geometric procedure by Gubser and Yarom, which starts from a static, maximally symmetric flow on dS${}_3\times \mathbb{R}$. Three foliations of dS${}_3$ preserve three-dimensional non-Abelian isometry groups, namely, the flat ISO(2)-invariant, the spherical (closed) SO(3)-invariant, and the hyperbolic (open) SO(2,1)-invariant slicings. I show that the fluids that preserve these symmetries, after they have been Weyl transformed to flat spacetime, give rise to three physically distinct and boost-invariant solutions of the relativistic dissipative Navier-Stokes equations: the well-known and widely studied Bjorken and Gubser flows, and a seemingly thus far unexplored solution that arises from the hyperbolic slicing of dS${}_3$. The new solution combines the radial expansion characteristic of the Gubser flow with the late-proper-time applicability of Bjorken's solution, and features a finite, radially bounded droplet whose expanding edge resembles a free-streaming shockwave.

Comments: v2: 11 pages, 3 figures. Typo fixed and references added