Newton's inverse-square law has a hidden assumption: gravity spreads
spherically through area 4πr². What if that's wrong for disk galaxies?
The core idea:
For a thin rotating disk, feedback drives matter into the disk plane and
confines gravitational flux cylindrically. Effective area becomes 4πHr
instead of 4πr², giving g ∝ 1/r → flat rotation curve. No dark matter.
The general law: g(r) = GM / A_eff(r)
Why feedback?
Like water carving a channel — a density fluctuation concentrates flux,
which draws more matter, which deepens the potential, which concentrates
flux further. The loop runs until a stable flat disk forms. Disk geometry
then confines flux to the plane. Cylindrical propagation is the *result*
of feedback, not a separate assumption.
The NFW profile falls out analytically:
The "missing gravity" between cylindrical and spherical propagation is:
***Δg(r) = [GM/4πr²] × (***r/H − 1)
Attribute this to an unknown mass distribution via Poisson's equation → you
get ρ_DM ∝ 1/r² — the NFW profile — derived in three lines without
simulation. The halo isn't a substance; it's what spherical equations see
when looking at a cylindrical system.
The feedback threshold:
Feedback switches on when f_obs > f_crit = H/R (disk aspect ratio).
Solar system: f = 0.001, f_crit = 0.025 → no feedback → Newton exact.
Milky Way: f = 3.6, f_crit = 0.020 → 180× above threshold → flat rotation.
This threshold also defines the domain of validity of Newton's law.
Testable prediction:
Lensing amplification in the disk plane: α_eff = α_GR × (r/H) ≈ 33×.
Edge-on galaxies should lens 33× stronger than face-on galaxies of the same mass. Dark matter halos (spherical) predict no such anisotropy. Testable with Euclid weak-lensing data stratified by inclination.
Limits I acknowledge:
Galaxy cluster lensing remains an open problem — spherical clusters get no
amplification from this mechanism. Not peer-reviewed.
Full derivations:
https://zenodo.org/records/20045684
Appreciate for any feedback.