Vorticity in analog gravity

Abstract

In the analog 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 curved space-time. 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 that 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 a straightforward extension in order to go beyond the irrotational constraint. Using a charged—relativistic and nonrelativistic—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 flow velocity in the presence of vorticity.

Analogue black holes in relativistic BECs: Mimicking Killing and universal horizons

“…where U ≡ λ(φ * φ) 2 and U ′ = dU/dφ. At the linearized perturbations level, and under suitable assumptions, the charged phonons propagate under an effective acoustic metric [34]. Nevertheless, following our prescription and relating the acoustic metric to the fluid flow u µ and the aether to the gauge field A µ , will lead us to an inconsistent scenario where the properties of the aether (including the existence of possible universal horizons) are mere gauge effects.…”

“…Other gauge couplings would suffer from the same disease. We note, however, that although gauge couplings cannot be used to simulate analogue universal horizons, they provide a natural way to incorporate vorticity in analogue systems [34].…”

“…Making use of the continuity equation and neglecting the quantum potential T ρ under the same assumptions as in Ref. [34], Eq. (71) takes the form…”

Accelerated observers emerging from a Bose-Einstein condensate through analogue gravity

“…The analysis of the speed of sound in a fluid and the possibility of shaping it in the form of the equation of motion for a non-massive field immersed in a curved space-time is already an old result [1], which leads to an equation of motion for the corresponding velocity potential that can be expressed as an equation of motion for a minimally-coupled scalar field, without mass, which propagates in a Lorentzian geometry. Some generalizations of this result, such as the possibility of having a rotational fluid, [5,6,7,8], or the case of an irrotational viscous fluid [9], have also been carried out.…”

Analog gravity in nonisentropic fluids

“…The effective metric (1) has been originally derived for an isentropic irrotational perfect fluid. However, it has been recently demonstrated that the condition of vanishing vorticity can be relaxed for a Bose Einstein condensate coupled to the electromagnetic field [8].…”