Electromagnetic Fields and Charged Defects in a Superfluid Defect Toy Model

We extend a previously developed superfluid defect toy model of gravity to include electromagnetism. The vacuum is modeled as a compressible superfluid, and massive bodies are identified with throat-like flux-tube defects that drain the vacuum and may carry circulation. In earlier work we showed that the acoustic metric of this fluid, together with suitable defect profiles, reproduces Newtonian gravity, 1PN orbital dynamics, gravitational optics, spin precession, and the Einstein–Infeld–Hoffmann 𝑁-body Lagrangian. Here we introduce a hydrodynamic dictionary that identifies an effective electromagnetic scalar and vector potential with combinations of the enthalpy and velocity fields, so that the magnetic field is proportional to vorticity (confined to defect cores in the present irrotational-bulk limit) and the electric field is minus the Euler acceleration. With this identification the homogeneous Maxwell equations become kinematic identities, while the inhomogeneous equations follow from a sourced acoustic wave equation for the four-potential in Lorenz gauge, with dyon defects providing the four-current. The static breathing mode of a defect throat generates a Coulomb 1∕r potential with radius-independent Gauss flux, and the Lorentz force on charged defects is shown to coincide with the Magnus and pressure forces on vortices. The same geometric data that determine the gravitational mass — the throat radius, length, and circulation — also fix the effective electric charge and imply an electromagnetic/gravitational force hierarchy that scales as 1∕a² with the throat radius.