Vorticity in analogue gravity

TL;DR

This paper extends the analogue gravity framework to include vorticity by deriving an acoustic metric for charged Bose--Einstein condensates, allowing the study of rotational flows in analogue gravity models.

Contribution

It introduces a method to incorporate vorticity into the acoustic metric in analogue gravity using charged Bose--Einstein condensates.

Findings

Derived a d'Alembertian equation for charged phonons with vorticity.

Extended the analogue gravity framework beyond irrotational flows.

Showed the emergent metric depends on flow velocity with vorticity.

Abstract

In the analogue gravity framework, the acoustic disturbances in a moving fluid can be described by an equation of motion identical to a relativistic scalar massless field propagating in a curved spacetime. This description is possible only when the fluid under consideration is barotropic, inviscid and irrotational. In this case, the propagation of the perturbations is governed by an acoustic metric which depends algebrically on the local speed of sound, density and the background flow velocity, the latter assumed to be vorticity free. In this work we provide an straightforward extension in order to go beyond the irrotational constraint. Using a charged --- relativistic and non-relativistic --- Bose--Einstein condensate as a physical system, we show that in the low momentum limit and performing the eikonal approximation we can derive a d'Alembertian equation of motion for the charged phonons where the emergent acoustic metric depends on a flow velocity in the presence of vorticity.