Analogue gravitational field from nonlinear fluid dynamics

TL;DR

This paper explores how the inherent nonlinearity of fluid dynamics influences the analogue gravitational fields experienced by sound waves, with implications for Bose-Einstein condensate experiments.

Contribution

It derives the effects of fluid nonlinearity on the effective spacetime metric for sound waves and proposes observable consequences in ultracold gas experiments.

Findings

Nonlinearity modifies the effective gravitational field experienced by sound.

Analytical tools like Riemann invariants reveal source terms from nonlinearity.

Predicted effects are observable in Bose-Einstein condensate setups.

Abstract

The dynamics of sound in a fluid is intrinsically nonlinear. We derive the consequences of this fact for the analogue gravitational field experienced by sound waves, by first describing generally how the nonlinearity of the equation for phase fluctuations back-reacts onto the definition of the background providing the effective space-time metric. Subsequently, we use the the analytical tool of Riemann invariants in one-dimensional motion to derive source terms of the effective gravitational field stemming from nonlinearity. Finally, we show that the consequences of nonlinearity we derive can be observed with Bose-Einstein condensates in the ultracold gas laboratory.