A Geometric View of Gravity (Frome Disks to Rings)
From Disks to Rings: A Geometric View of Gravity
📌 Update — May 2026
This post was an early exploration of gravitational geometry that pointed in an interesting direction. The intuition behind it has since been substantially rethought and rebuilt from the ground up.
The current framework — Gravitational Flux Area and the Self-Reinforcing Feedback Principle — replaces the bowl geometry with a more rigorous and physically grounded set of principles.
Readers are encouraged to go directly to the updated post: → [here]
What if gravity isn’t about pulling harder…
but about spreading less?
This post introduces a simple geometric idea that may help explain one of the most puzzling observations in astrophysics:
why galaxies rotate the way they do.
🔠The Puzzle: Flat Rotation Curves
In a simple Newtonian picture, gravity weakens with distance:
g(r) ≈ 1 / r^2
So stars farther from the center of a galaxy should move more slowly.
But observations show something very different.
👉 Galaxy rotation curves are flat.
Stars far away move almost as fast as those closer in.
This is usually explained by introducing dark matter.
But what if there’s another way to look at it?
🌀 A Different Idea: It’s About Geometry
Instead of changing the amount of mass,
let’s change how gravity spreads.
Imagine that gravity doesn’t simply spread through flat space,
but follows paths in an effective geometry.
We call this the bowl geometry.
🥣 The Bowl Picture
Now look at the diagram.
The galaxy sits at the center
Gravity flows outward (yellow lines)
But instead of spreading in flat space, it follows the bowl-shaped geometry
At small distances, the bowl is almost flat.
👉 So gravity spreads evenly in all directions.
🔵 Inner Region: Disk-like Spreading
Near the center:
The geometry is nearly flat
Gravity spreads like a full disk (or sphere in 3D)
Effective area ≈ Ï€ * r^2
g(r) ≈1 / r^2
✔ This matches standard gravity
🟡 Outer Region: Ring-like Spreading
Far from the center:
The geometry subtly changes
Paths begin to align (this is the key!)
Instead of spreading everywhere, gravity flows more along preferred paths.
Now the effective cross section looks like a ring:
Effective area ≈ 2 * Ï€ * r * w(r)
g(r) ≈1 / r
🔥 The Key Insight
Gravity doesn’t get stronger — it spreads less.
🧠Why Do Paths Align?
This comes from a simple geometric idea:
👉 Paths tend to follow shortest or most efficient routes.
In geometry, these are called geodesics.
You don’t need the math to understand this.
Think of it like this:
On a flat surface → you can go in any direction equally
On a slightly curved surface → over long distances, some paths become more efficient
So:
Over long distances, propagation naturally selects certain directions.
This is what creates the channeling effect.
🔄 Disk → Ring Transition
This is the most important part of the model.
Inner region → disk-like spreading
Outer region → ring-like spreading
Disk → Ring transition = change in gravity behavior
🌊 A Helpful Analogy (The “Water Level”)
Imagine the bowl is partially submerged in water.
The boundary where it meets the surface defines a radius (r_0)
Inside → full area (disk-like)
Outside → only a band (ring-like)
As mass increases:
👉 The bowl “sinks deeper”
👉 The transition radius moves outward
r_0 ≈ sqrt(M)
🧠Big Picture
This model suggests:
Gravity is not just a force
It is a propagation process shaped by geometry
📌 Final Takeaway
Flat rotation curves may arise from reduced spreading, not extra mass
🚀 Why This Matters
This is not a replacement for existing theories,
but an alternative perspective:
👉 What if gravity behaves differently at large scales
because of how it propagates?
If you found this interesting, I’d love to hear your thoughts.
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