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Hydrodynamics in the Carrollian regime

Kedar S. Kolekar, Taniya Mandal, Ashish Shukla, Pushkar Soni

TL;DR

The work develops hydrodynamics in the Carrollian regime by retaining subleading $O(c^2)$ terms in a double expansion with the hydrodynamic derivative series. Using the Papapetrou-Randers geometry, the authors derive perfect-fluid and viscous Carroll equations to all orders in the Carroll expansion and apply them to corrections of Bjorken and Gubser flow, uncovering explicit rapidity-dependent modifications. The results provide a systematic framework for including departures from exact boost-invariance in ultrarelativistic flows, offering potentially improved analytic descriptions of quark-gluon plasma dynamics and a path toward more general Carrollian hydrodynamics. The study also outlines future directions, including connections to entropy currents, pre-ultra-local variables, and symmetry structures of subleading Carroll terms.

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.

Hydrodynamics in the Carrollian regime

TL;DR

The work develops hydrodynamics in the Carrollian regime by retaining subleading terms in a double expansion with the hydrodynamic derivative series. Using the Papapetrou-Randers geometry, the authors derive perfect-fluid and viscous Carroll equations to all orders in the Carroll expansion and apply them to corrections of Bjorken and Gubser flow, uncovering explicit rapidity-dependent modifications. The results provide a systematic framework for including departures from exact boost-invariance in ultrarelativistic flows, offering potentially improved analytic descriptions of quark-gluon plasma dynamics and a path toward more general Carrollian hydrodynamics. The study also outlines future directions, including connections to entropy currents, pre-ultra-local variables, and symmetry structures of subleading Carroll terms.

Abstract

Carroll hydrodynamics arises in the 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 limit of relativistic hydrodynamics, we perform a small- 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.
Paper Structure (14 sections, 93 equations, 1 figure)

This paper contains 14 sections, 93 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Basic setup
  3. The hydrodynamic derivative expansion vs. the $c\to 0$ limit
  4. The Papapetrou-Randers parametrization
  5. Perfect fluids in the Carrollian regime
  6. Perfect fluid equations to all orders in the $c\to 0$ expansion
  7. Viscous effects in the Carrollian regime
  8. First order derivative corrections in the Carrollian regime
  9. Applications
  10. Computing corrections to Bjorken flow
  11. Computing corrections to Gubser flow
  12. Discussion and outlook
  13. Local Carroll boost invariance of the hydrodynamic equations
  14. Second order derivative corrections for a conformal Carroll fluid

Figures (1)

  • Figure 1: A pictorial representation for the emergence of Carrollian physics in the Bjorken and Gubser flow models of QGP. The collision event takes place at the origin, with the Milne patch representing its forward light cone. The ultrarelativistic nature of the flow lands one in the near-horizon region, where local lightcones collapse, or effectively $c\to 0$, thereby making the dynamics Carrollian.