Spin, Vorticity, and N-Body Dynamics in a Superfluid Defect Toy Model

We extend our superfluid–defect toy universe to spin and full N–body dynamics at 1PN order. The vacuum is a compressible superfluid and massive bodies are flux–tube “throat” defects that exchange mass/flux with the medium (effective sinks in the 3D description). Earlier papers fixed the orbital sector (β=3) and selected a stiff n=5 equation of state from optical 1PN observables. Here we promote defects to composite “dyons” (sink + vortex ring). Their far–field circulation defines a gravitomagnetic vector potential with the correct J/r3 scaling, reproducing the Lense–Thirring effect and fixing the vortex–spin calibration by matching the Kerr weak–field limit. In the N–body problem, density–dependent masses reproduce the static G2 three–body term of the Einstein–Infeld–Hoffmann (EIH) Lagrangian. The remaining velocity–dependent EIH cross terms arise from overlap energy of translational wakes. Using an isotropic projector decomposition into longitudinal and transverse solenoidal (vortical) components (with an optional helical mode), we match the full EIH cross–term tensor with real parameters: aH=0, α2=3/4, and K=2/π2. The positive value α2=3/4 makes the quadratic wake functional positive–definite, showing that earlier imaginary couplings were artifacts of an incomplete wake basis. Subject to the dynamical requirement that moving sink defects generate a long–range wake u∝1/r2 (equivalently u(k)∝1/k), the model reproduces GR’s 1PN scalar, optical, spin, and vector dynamics while remaining consistent with the calibrated orbital sector and optical tests.