Hydrodynamics in the Carrollian regime

TL;DR

This paper develops a detailed framework for Carrollian hydrodynamics by expanding relativistic hydrodynamics in small speed of light, including subleading terms, and applies it to models relevant in heavy-ion collision physics.

Contribution

It introduces a small-$c$ expansion of relativistic hydrodynamics that retains subleading terms, extending the understanding of Carrollian fluids beyond leading order.

Findings

Derived modified flow equations with rapidity dependence

Applied formalism to perfect and viscous fluids

Provided insights into ultrarelativistic flow models

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.