Relativistic Fluids, Hydrodynamic Frames and their Galilean versus Carrollian Avatars

Abstract

We comprehensively study Galilean and Carrollian hydrodynamics on arbitrary backgrounds, in the presence of a matter/charge conserved current. For this purpose, we follow two distinct and complementary paths. The first is based on local invariance, be it Galilean or Carrollian diffeomorphism invariance, possibly accompanied by Weyl invariance. The second consists in analyzing the relativistic fluid equations at large or small speed of light, after choosing an adapted gauge, ADM-Zermelo for the former and Papapetrou-Randers for the latter. Unsurprisingly, the results agree, but the second approach is superior as it effortlessly captures more elaborate situations with multiple degrees of freedom. It furthermore allows to investigate the fate of hydrodynamic-frame invariance in the two limits at hand, and conclude that its breaking (in the Galilean) or its preservation (in the Carrollian) are fragile consequences of the behaviour of transport attributes at large or small $c$. Both methods do also agree on the doom of Noetherian currents generated in the relativistic theory by isometries: non-trivial currents are not always guaranteed in Newton-Cartan or Carroll spacetimes as a consequence of Galilean or Carrollian isometries. Comparison of Galilean and Carrollian fluid equations exhibits a striking but often superficial resemblance, which we comment in relation to black-hole horizon dynamics, awkwardly akin to Navier-Stokes equations. This congruity is authentic in one instance though and turns out then to describe Aristotelian dynamics, which is the last item in our agenda.

v1: 1+96 pages, Latex, v2: JHEP version

References in corpus (16)

• The BMS/GCA correspondence
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Flat Holography: Aspects of the dual field theory
• Non-relativistic conformal symmetries and Newton-Cartan structures
• Conformal Carroll groups
• Dynamics of Carroll Particles
• Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry
• Field Theories with Conformal Carrollian Symmetry
• Stable and causal relativistic Navier-Stokes equations
• On the convergence of the gradient expansion in hydrodynamics
• Galilean Isometries
• Revisiting non-relativistic limits
• Aspects of hot Galilean field theory
• Torsional Newton-Cartan Geometry from the Noether Procedure
• On asymptotic symmetries in higher dimensions for any spin

Cited by in corpus (1)

• One-Dimensional Carrollian Fluids III: Global Existence and Weak Continuity in $L^{\infty }$