Non-boost invariant fluid dynamics

Abstract

We consider uncharged fluids without any boost symmetry on an arbitrary curved background and classify all allowed transport coefficients up to first order in derivatives. We assume rotational symmetry and we use the entropy current formalism. The curved background geometry in the absence of boost symmetry is called absolute or Aristotelian spacetime. We present a closed-form expression for the energy-momentum tensor in Landau frame which splits into three parts: a dissipative (10), a hydrostatic non-dissipative (2) and a non-hydrostatic non-dissipative part (4), where in parenthesis we have indicated the number of allowed transport coefficients. The non-hydrostatic non-dissipative transport coefficients can be thought of as the generalization of coefficients that would vanish if we were to restrict to linearized perturbations and impose the Onsager relations. For the two hydrostatic and the four non-hydrostatic non-dissipative transport coefficients we present a Lagrangian description. Finally when we impose scale invariance, thus restricting to Lifshitz fluids, we find 7 dissipative, 1 hydrostatic and 2 non-hydrostatic non-dissipative transport coefficients.

Null reductions of the M5-brane

“…In contrast, the field theories we obtain do not have higher derivatives but involve Lagrange multiplier constraints that reduce the dynamics to motion on a moduli space of anti-selfdual gauge fields [9,10], in line with the DLCQ description of the M5-brane [11,12]. Other classes of theories without Lorentz invariance but related to String/M-Theory have recently received attention in works such as [13][14][15][16][17][18].…”

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].…”

Geometrizing non-relativistic bilinear deformations

“…It was first obtained as a geometrization of Newtonian spacetime by Cartan [23,24], but has seen a revival in recent years. There is extensive literature on the subject and its applications to a wide selection of areas such as generalized holography [26,[32][33][34][35][36][37][38][39][40][41][42], condensed matter theory [29,[43][44][45][46][47], hydrodynamics [48][49][50][51][52][53][54], string theory [55][56][57][58][59][60][61][62][63] and more [64][65][66][67][68]. We shall consider the 2-dimensional gravity relevant to our aims.…”