Warped space-time for phonons moving in a perfect non- relativistic fluid

– We construct a kinematical analogue of superluminal travel in the “warped” space-times curved by gravitation, in the form of “super-phononic” travel in the effective spacetimes of perfect nonrelativistic fluids. These warp-field space-times are most easily generated by considering a solid object that is placed as an obstruction in an otherwise uniform flow. No violation of any condition on the positivity of energy is necessary, because the effective curved space-times for the phonons are ruled by the Euler and continuity equations, and not by the Einstein field equations. Introduction. – The concept of “warp fields”, or faster than light (FTL) propagation/travel, is usually relegated into the realm of science fiction literature. Taking warp fields more seriously, when trying to develop physical realizations within the context of Einstein gravity, one has to face the difficulty that fulfilling the Einstein equations demands “exotic matter”; matter violating the null, weak, strong, and dominant conditions on the positivity of energy [1, 2, 3, 4, 5]. If, on the other hand, one allows for negative energy densities (which occur for example in the quantum vacuum of the Casimir effect) the energy densities (and to a lesser degree the total energies [6]) actually required to construct macroscopic warp drives are astronomical [7]. One way of side-stepping these problems, and developing a concrete physical model of what a warp field might look like, is to consider effective space-time theories originating in condensed matter [8, 9]: A flowing hydrodynamical background governed by the nonrelativistic Euler and continuity equations represents a curved space-time for the quasiparticle excitations moving in the fluid. The role of the speed of light is played by the speed of sound, and superluminal travel turns into super-phononic propagation due to the effective space-time curvature. The necessity of violating the energy conditions is no longer given, because the effective pseudo-Riemannian space created by the laboratory flow in absolute Newtonian space is determined by the equations of nonrelativistic hydrodynamics, and not by the Einstein field equations.