Gravitational Optics and Soliton Geodesics in a Superfluid Defect Toy Model

We extend a previously developed superfluid-defect toy model of gravity from orbital dynamics to the full suite of classic 1PN tests involving light and clocks. The model treats the vacuum as a compressible superfluid and massive bodies as flux-tube defects that drain this vacuum; Paper 1 showed that an exactly Newtonian scalar sector together with a position-dependent kinetic prefactor σ(r) reproduces the GR perihelion precession and fixes a single orbital parameter β = 3. Here we focus on gravitational optics and redshift. We model the vacuum as a stiff (n = 5) polytropic superfluid and show that a flux-tube mass defect induces a 1/r pressure and density deficit that fixes a refractive index profile N(r) governing light bending and Shapiro delay. Requiring this profile to reproduce the GR lensing coefficient uniquely selects n = 5 and implies the standard PPN value γobs = 1 as inferred from optical observables. Because the optical construction packages curvature entirely into the spatial part of the line element with gtt(opt) = −1, a naive PPN read-off of the optical metric alone would instead assign γopt = 2; this distinction underlies the “10 vs 6” tension discussed below. If defects were to follow this bare acoustic metric, the predicted perihelion advance would have coefficient 10 instead of the GR value 6. We show that treating defects as hydrodynamically dressed solitons resolves this tension: the static density deficit and the coherent dipole flow around a moving throat contribute κρ = 1 and κadd = 1/2. The remaining pressure–volume (breathing) inertia is parameterized by κPV, which is fixed by the orbital calibration to κPV = 3/2 so that β = κρ + κadd + κPV = 3; a microphysical derivation of κPV is left for future work. Within the 1PN, weak-field regime the combined orbital, optical, and redshift sectors of the toy model are therefore indistinguishable from Schwarzschild, demonstrating that light and matter probe distinct acoustic and hydrodynamic projections of the same brane–bulk geometry (a bi-metric structure), which resolves the apparent tension in spatial curvature coefficients.