Abstract
We present a systematic treatment of perfect fluids with translation and rotation symmetry, which is also applicable in the absence of any type of boost symmetry. It involves introducing a fluid variable, the kinetic mass density, which is needed to define the most general energy-momentum tensor for perfect fluids. Our analysis leads to corrections to the Euler equations for perfect fluids that might be observable in hydrodynamic fluid experiments. We also derive new expressions for the speed of sound in perfect fluids that reduce to the known perfect fluid models when boost symmetry is present. Our framework can also be adapted to (non-relativistic) scale invariant fluids with critical exponent zz. We show that perfect fluids cannot have Schrödinger symmetry unless z=2z=2. For generic values of zz there can be fluids with Lifshitz symmetry, and as a concrete example, we work out in detail the thermodynamics and fluid description of an ideal gas of Lifshitz particles and compute the speed of sound for the classical and quantum Lifshitz gases.
Highlights
We focus on perfect fluids
The first main result of this paper is to show how the kinetic mass density enters the formulation of perfect fluids, and to find an explicit form of the energy-momentum tensor in the absence of boost symmetry
We turn to the fluid description, in which we eventually perturb away from global equilibrium by varying all quantities in space and time. We do this for perfect fluids, i.e. maintaining local equilibrium, whose energy-momentum tensor we define in the rest or laboratory frame
Summary
Perfect fluids are fluids that at rest are completely described in terms of their energy density and pressure P. The first main result of this paper is to show how the kinetic mass density enters the formulation of perfect fluids, and to find an explicit form of the energy-momentum tensor in the absence of boost symmetry. The sound speed needs to be computed for arbitrary background fluid velocities, since one cannot rely on the Doppler effect that relates the sound speeds in different frames This analysis is performed in this paper and is the second of our main results.
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