Hydrodynamics in the Carrollian regime

Abstract

Carroll hydrodynamics arises in the $c\to 0$ limit of relativistic hydrodynamics. Instances of its relevance include the Bjorken and Gubser flow models of heavy-ion collisions, where the ultrarelativistic nature of the flow makes the physics effectively Carrollian. In this paper, we explore the structure of hydrodynamics in what can be termed as the Carrollian regime, where instead of keeping only the leading terms in the $c\to 0$ limit of relativistic hydrodynamics, we perform a small-$c$ expansion and retain the subleading terms as well. We do so both for perfect fluids as well as viscous fluids incorporating first order derivative corrections. As apposite applications of the formalism, we utilize the subleading terms to compute modifications to the Bjorken and Gubser flow equations which bring in, in particular, dependence on rapidity.

v1: 31 pages, 1 figure; v2: Minor modifications and improvements, several additional references; v3: Added discussion about various symmetries involved in section 5, added a new appendix demonstrating local Carroll boost invariance of the hydrodynamic equations, added a reference; v4: Reference added; v5: additional discussion added in appendix A, published in IJMP-A