Emergent spacetime geometries and nonlinear acoustic waves in photon-fluids
The propagation of finite-amplitude waves in defocusing media is investigated in the framework of the hydrodynamic description of light as a photon fluid. We show that in the appropriate limits, the wave dynamics can described in purely geometrical terms, where an effective curved spacetime determining the propagation of the waves is generated by the waves themselves. The spacetime geometry emerges naturally as a result of the interaction between a density wave and the self-induced background flow. Remarkably, a similar situation occurs in General Relativity: mass distributions evolve in a curved spacetime metric that is modified by mass itself.
In this context, we offer an alternative view of some nonlinear effects in acoustic waves propagation. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and the subsequent formation of a shock. We show that the self-steepening effect can be interpreted as a kind of gravitational influence on the wave by its own effective metric, while the wave-breaking process is associated to the formation of a curvature singularity.