A preferred reference frame <i>S</i> _<i>V</i> associated with critical speed of a superfluid: A new acoustic causal structure

Abstract We investigate the stability of the causal structure—generated by the introduction of a preferred reference frame—which in turn, is associated with the critical speed of a Landau superfluid and represents the cosmological vacuum. We discuss the acoustic geometry associated with the set of excited states and their relation to the Refractive Index Perturbation (R.I.P.). We show that the presence of the privileged reference frame implies kinematic transformations and velocity compositions that contain, in an upper limit, the properties of Lorentz symmetry and the critical velocity of the superfluid as a lower limit. We treat the critical speed in an Euler reference frame, showing its relation with a convective term, as well as the possibility of deducing a Navier-Stokes equation modified by a quantum potential—linked to the deformation of the momentum generated by the drag of the superfluid with critical speed. Establishing a hydrodynamic reference, where the phase transition occurs, ‘destroys’ superfluids. The conserved properties of this superfluid were studied. The study of the transformations from an Einstein-Euler reference frame to the preferred reference frame allows us to recover the previously defined acoustic geometry. The study of the causal structure of this acoustic geometry indicated the existence of an ergoregion, confirming what we found as a convective term. Thus, we have a stable causal structure, both because of the method defined for acoustic geometries—and because of the fear of Hydrodynamic Modes. Therefore we can categorically state that the preferred reference frame induces a stable causal structure.