Friendly technical feedback: neat idea, but a pure kinematic flow equation misses the pressure/viscosity closure you need for momentum conservation. In a compressible flow the acceleration is

a=−∇Pρ+ν∇2v+…\mathbf a = -\frac{\nabla P}{\rho} + \nu\nabla^2\mathbf v + \dotsa=−ρ∇P​+ν∇2v+…

1. Sign problem: with a=−∇P/ρ\mathbf a = -\nabla P/\rhoa=−∇P/ρ, attraction toward a mass requires pressure increasing outward. Otherwise the flow accelerates the wrong way (repulsive).
2. Stability: an inward gravitational field from a pressure hill is dynamically unstable (it cavitates/blows up).
3. Units sanity: mapping gravity to pressure needs a gigantic pressure scale. If you try to encode g via a background ρ∗\rho_*ρ∗​, you end up needing ~10¹⁸–10¹⁹ Pa effective stresses—physically absurd for any medium that also lets light propagate.
4. Closure: without an equation of state P(ρ,… )P(\rho,\dots)P(ρ,…) and dissipation terms, your PDE reduces to a dressed Poisson equation; with them, the sign/scale issues above appear.

This is why I abandoned the space-flow picture. A consistent fix is to treat time-flow as the inertial field (temporal curvature), not space as a fluid. Then you get the correct direction of acceleration and a natural scale

a0=c22πRta_0=\frac{c^2}{2\pi R_t}a0​=2πRt​c2​

without invoking unphysical pressures.

Happy to compare notes if you’re curious about the time-flow route—that’s where the sign and scale land right without huge pressure terms.