Two-Fluid Hydrodynamics

The analog of matter in the background of superfluid vacuum consists of quanta of sound waves (phonons), which form a dilute gas. This gas of quasiparticles represents the so-called normal component of the liquid, which bears all the entropy of the liquid. In a local equilibrium, the normal component is characterised by temperature and its velocity. The two-fluid hydrodynamics is the system of equations describing the motion of two subsystems — the superfluid vacuum and normal component. Dynamics of normal component fully reproduces the dynamics of relativistic matter in the presence of a...

The analog of matter in the background of superfluid vacuum consists of quanta of sound waves (phonons), which form a dilute gas. This gas of quasiparticles represents the so-called normal component of the liquid, which bears all the entropy of the liquid. In a local equilibrium, the normal component is characterised by temperature and its velocity. The two-fluid hydrodynamics is the system of equations describing the motion of two subsystems — the superfluid vacuum and normal component. Dynamics of normal component fully reproduces the dynamics of relativistic matter in the presence of a gravity field. Though the corresponding ‘Einstein equations’ for ‘gravity’ itself are not covariant, by using the proper superflow fields many phenomena related to the classical and quantum behavior of matter in curved spacetime can be simulated, including black-hole physics. This chapter also considers energy momentum tensor for matter, effective acoustic metric, the meaning of covariant and contravariant components of 4-momentum, particle current and quasiparticle momentum, normal and superfluid densities, global and local thermodynamic equilibrium, Tolman's law, and event horizon.