First order non-Lorentzian fluids, entropy production, and linear instabilities

Abstract

In this paper, we investigate linear instabilities of hydrodynamics with corrections up to first order in derivatives. It has long been known that relativistic (Lorentzian) first order hydrodynamics, with positive local entropy production, exhibits unphysical instabilities. We extend this analysis to fluids with Galilean and Carrollian boost symmetries. We find that the instabilities occur in all cases, except for fluids with Galilean boost symmetry combined with the choice of macroscopic variables called Eckart frame. We also present a complete linearized analysis of the full spectrum of first order Carrollian hydrodynamics. Furthermore, we show that even in a fluid without boost symmetry present, instabilities can occur. These results provide evidence that the unphysical instabilities are symptoms of first order hydrodynamics, rather than a special feature of Lorentzian fluids.

Effective field theory for hydrodynamics without boosts

“…We would like to point out that the linear mode analysis presented above has been done at finite equilibrium fluid velocity u i = u i 0 , and yet we do not encounter any additional gapped unphysical poles in the upper-half complex ω plane. This is in contrast to the Landau and Eckart frames typically employed in relativistic hydrodynamics, that are unstable in a finite fluid-velocity state; see [30,31]. This affirms that the density frame introduced in this paper is a stable hydrodynamic frame, applicable to hydrodynamic theories with arbitrary boost symmetry structure -Galilean, Lorentzian, or absence thereof.…”

“…In contrast with all the previous literature, we present our results in a new hydrodynamic frame, which we call density frame, that is linearly stable (in the sense of [30][31][32]) irrespective of the boost symmetry in place (Galilean or Lorentzian), or absence thereof, and is thus better suited for potential numerical simulations. This frame choice aligns the fluid velocity with the flow of momentum, rather than the flow of internal energy (as in the Landau frame) or charge/particle-number (as in the Eckart frame).…”

Gauges in three-dimensional gravity and holographic fluids

“…Assuming the latter exist, the study of their hydrodynamic regime calls for a theory of Carrollian fluids. Discussions or attempts for designing Carrollian (or generalized Galilean) hydrodynamics can be found in [70][71][72][73][74][75][76][77]. A comprehensive study was performed in [78].…”

Driven black holes: from Kolmogorov scaling to turbulent wakes

“…This should be contrasted with the usual treatment of hydrodynamics in a dynamical setting, where one typically truncates at a finite order and treats the resulting system of equations as exact -a procedure which fundamentally changes the theory. As a consequence of this change one discovers physically undesirable qualities such as instabilities and acausal behaviour both for relativistic theories [38], and non-relativistic theories [39]. Furthermore, one must of course also verify post-hoc that the solution remained a good approximation within the framework of a perturbative gradient expansion.…”