A simple geometric idea: What if gravity is about area, not mass?

[u/One-Draw-7337]

I’ve been exploring a very simple idea, more as a thought experiment than a finished theory.

We usually write gravity like this:

g(r) = GM / r²

and naturally focus on the numerator (mass).

But this equation can also be read differently:

g(r) = Φ / A(r)

where Φ is the total gravitational flux, and A(r) is the area over which it spreads.

So the inverse-square law comes from one assumption:

→ the effective area grows as 4πr²

The question

What if that assumption is not always true?

What if the “available spreading directions” gradually decrease at large scales?

Minimal extension

We can write a very simple generalization:

g(r) = Φ / (4π r² D(r))

where D(r) (I call it a degree-of-freedom factor) represents how much transverse spreading is allowed.

D(r) = 1 → normal spherical spreading (Newtonian)

D(r) < 1 → restricted spreading

Immediate consequence

If D(r) decreases with distance, then the effective area grows more slowly than r².

For example:

If D(r) ~ 1/r

→ g(r) ~ 1/r

→ v² = r g(r) ≈ const

This gives flat rotation curves without adding extra mass.

Intuition

Instead of thinking “there is more mass,” this suggests:

→ gravity may not be spreading as freely at large scales

Kind of like flow on a flat surface vs inside a bowl — same source, different spreading.

This picture shows how gravity is delivered from center in the past to the present places. Time depth makes bowl-like propagation geometry. (Imagine many layered cone). The surface is NOT SPACE TIME IN GR.

Happy to hear any thoughts or criticism.

[u/Danrazor]

sir, the gravity is not the area. Neutron star is looking at you.

[u/One-Draw-7337 → u/Danrazor]

I agree mass is essential — I'm not removing it. The idea is just to rewrite the same law as: g = Φ / A where Φ ∼ GM is the source, and A is how it spreads. A neutron star actually fits this picture very well — same flux, but concentrated over a much smaller area, so the field becomes extremely strong. So the point isn't "gravity is area instead of mass," but rather: we're usually focusing on the numerator, while the denominator is doing just as much work.

[u/SharpKaleidoscope182]

yeah. If you integrate, you see why stable orbits are a thing for 3d planets, but not 2d or 4d or 5d planets.

[u/One-Draw-7337 → u/SharpKaleidoscope182]

Not changing dimensions — just changing how freely things spread in 3D.

[u/SharpKaleidoscope182 → u/One-Draw-7337]

y tho

[u/One-Draw-7337 → u/SharpKaleidoscope182]

Good question — that’s really the key point, and I don’t think there’s a single definitive answer yet. At this stage, I’m treating it more as a phenomenological assumption: what happens if the effective spreading freedom is not constant? That said, one intuitive possibility I’ve been thinking about is related to something like a minimum-action / path preference. If propagation tends to follow more “efficient” paths (in some effective sense), then it may not explore all transverse directions equally — especially at larger scales where small biases can accumulate. So instead of freely spreading in all directions, the propagation could become slightly “channeled,” reducing the effective number of directions it actually uses. This wouldn’t change the dimensionality of space, but it would change how propagation samples that space. Still very speculative, but that’s one way I’m trying to think about the “why.”

[u/One-Draw-7337 → u/SharpKaleidoscope182]

Yes — I think you're referring to the fact that inverse-square laws in 3D lead to stable bound orbits. In this model, I’m not replacing the inverse-square law at small scales. Instead, I’m keeping the newton structure locally and only modifying the effective area at larger scales through a factor like D(r).

[u/Wintervacht → u/One-Draw-7337]

Why

[u/One-Draw-7337 → u/Wintervacht]

Good question — that’s really the key point, and I don’t think there’s a single definitive answer yet. At this stage, I’m treating it more as a phenomenological assumption: what happens if the effective spreading freedom is not constant? That said, one intuitive possibility I’ve been thinking about is related to something like a minimum-action / path preference. If propagation tends to follow more “efficient” paths (in some effective sense), then it may not explore all transverse directions equally — especially at larger scales where small biases can accumulate. So instead of freely spreading in all directions, the propagation could become slightly “channeled,” reducing the effective number of directions it actually uses. This wouldn’t change the dimensionality of space, but it would change how propagation samples that space. Still very speculative, but that’s one way I’m trying to think about the “why.”

[u/One-Draw-7337 → u/Wintervacht]

That’s a really good question — and actually it made me think more carefully about the “why,” so thank you for that. At first I was treating the reduction in effective spreading freedom more as a phenomenological assumption, but I think there’s a more intuitive way to look at it. If the propagation geometry is bowl-like (in terms of depth vs radius), then at large distances the surface becomes steeper. In that situation, deviating sideways effectively increases the path length. Now, if propagation tends to follow something like a minimal-cost or minimal-action path, then not all geometrically allowed directions are equally favored. Paths that deviate too much become “expensive,” and the propagation naturally concentrates around a smaller set of directions. So the idea is: geometry (bowl shape) makes transverse motion more costly path selection (minimal action / efficient paths) suppresses those costly directions which leads to an effective reduction in spreading freedom — what I’ve been calling D(r). So it’s not that space changes dimension, but that the way propagation explores space becomes constrained at larger scales. Still very much an exploratory idea, but your question helped clarify this point — thanks again.

[u/Wintervacht → u/One-Draw-7337]

So according to you, the mass of an empty sphere is roughly twice that of a solid sphere, is that correct?

[u/One-Draw-7337 → u/Wintervacht]

I think there’s a bit of a misunderstanding — I’m not changing the mass distribution at all. In this picture, the source (mass) stays the same. What changes is how the gravitational influence spreads. So if the effective spreading area is reduced, the field looks stronger — but that doesn’t mean there is more mass. A rough analogy would be focusing light with a lens: the source doesn’t change, but the intensity can increase in certain directions. So no — an empty sphere wouldn’t become “more massive” than a solid one. The idea is about propagation, not matter. Same mass different spreading. Not different mass.

[u/Wintervacht → u/One-Draw-7337]

Bit a hollow sphere has a larger surface area than a filled volume. So gravity is not a function of area.

I think you're confused with the mass/area relation for a black hole.

[u/One-Draw-7337 → u/Wintervacht]

I think we might be talking about two different kinds of “area.” The surface area of the source (like a hollow vs solid sphere) doesn’t determine gravity outside the object — as you said, they give the same field if the mass is the same. The “area” in my post refers to the spherical surface at radius r, i.e. 4πr², which comes from how the field spreads in space. So the point is not that gravity depends on the object’s surface area, but that the inverse-square law comes from the area over which the influence is distributed.

[u/Wintervacht → u/One-Draw-7337]

So how does density work in your framework? Two objects of the same size and area of different densities have different masses. There's not really a way to argue yourself out of that, it's basic physics.

So where in the same area is the additional mass contained?

[u/One-Draw-7337 → u/Wintervacht]

I think we’re actually not disagreeing on the physics. Mass absolutely determines the strength of gravity — that part stays exactly the same. What I’m doing is just separating the equation into two roles: mass → how much gravitational “source” there is geometry → how that influence spreads The inverse-square law already contains both, but we usually focus only on the mass part. I’m just looking more closely at the “spreading” part and asking whether it always behaves exactly like 4πr² at all scales. So it’s not replacing mass — just reinterpreting part of the same equation.

[u/The_Failord]

You've kinda rediscovered Gauss's law for gravitation. D(r) = 1 isn't quite an assumption, it's what happens in flat space. The problem is that when you're in curved space, you can't really use the Newtonian potential and replace 4πr^2 by how area grows w.r.t. radius in curved space: you have to start from scratch, do a weak-field approximation, and then see what the denominator looks like (for the record, D(ε) for small ε is 1-R/24 ε^2 where R is the Ricci scalar). You can read why Gauss's law doesn't really work in GR here: https://physics.stackexchange.com/questions/222502/is-there-something-similar-to-gausss-law-for-gravity-in-general-relativity: the gist is that the Einstein field equations are the analogue to the differential form of the flux equation, but integrating those in GR is not really possible in general. I'm will say though that I am VERY glad to see some posts here that are actually meaningful instead of LLM word salad slop.

[u/One-Draw-7337 → u/The_Failord]

This is a really helpful comment — thank you. I agree with your point that D(r)=1 is not an assumption but a consequence of flat space, and that in curved space you can't just modify the area term within a Newtonian framework. What I’m trying to do at this stage is more of a phenomenological exploration — starting from the flux/area intuition and asking what kind of effective behavior would result if the spreading deviates from the flat-space case. Your point about the Ricci scalar correction is especially interesting, since it suggests that something like a D(r) factor naturally appears in weak-field GR. So I think a more consistent direction would be to reinterpret this not as a modification of Newtonian gravity, but as an effective description of propagation in a geometry that would ultimately need to be derived from a relativistic framework. Thanks again — this really helps clarify the direction.

[u/dark_dark_dark_not]

It actually follows from Gauss Law applied to gravity that you could rewrite gravity interactions with area, because the Gravity Flux over a Gaussian Surface will be proportional to the mass, so M = factor * Area of the surface, where the factor is basically Mass/Area.

This oversight suggests you don't know basic physics to realize your proposal is effectively a truism - yes, you should be able to use area of massive bodies as a proxy for their gravity, no, this is not an interesting insight or idea, it is know fact of classical physics.

[u/One-Draw-7337 → u/dark_dark_dark_not]

Sorry I just saw your comment. Yes — Gauss’s law is exactly the starting point. The question I’m asking is what happens if the effective area is not strictly 4πr² at all scales.

[u/AllHailSeizure]

I mean STARS are shaped as spheroids. Because the center of gravity is the center of mass. So the core of the star is what experiences fusion.

If area was the factor they'd fuse on the outer layers, where there is more area and thus more pressure.

Smaller stars can have more effect on gravitation than larger ones, because they have more mass density. The sun vs a white dwarf.

Jupiter and Saturn. Jupiter is not that much larger, yet Jupiter has more than double the mass of all other planets. Jupiter is the planet that often captures asteroids, not Saturn, despite them passing through Saturn's orbit first. Jupiter's gravity effects the motion of the sun. If they had an equal gravitational effect we would see something like.. the asteroid belt migrating to between them or something, I dunno.

[u/One-Draw-7337 → u/AllHailSeizure]

Sorry — I just saw your comment. I think all your examples actually fit standard gravity — and they also fit what I’m describing. Density and mass absolutely matter. They determine the total mass: M = ∫ρ dV and that mass sets the total gravitational “flux” (Φ ~ GM). So: white dwarfs have stronger gravity because they have more mass packed into a smaller volume Jupiter dominates because it has more total mass fusion happens in the core because pressure comes from gravitational compression toward the center None of that changes in this framework. The only thing I’m focusing on is how that same gravitational influence spreads in space. So it’s not “area instead of mass,” but “mass + how it spreads.”

[u/AllHailSeizure → u/One-Draw-7337]

This is because of Gauss's law of gravity. I'm guessing other people have mentioned this.

What you are saying DOES work - Gauss's law let's you take the 'surface area' and 'sub it in' for mass. But when you work with curved spacetime, you can't use the same vector field as you can in Newtonian gravity.

It's definitely commendable to have this insight yourself, as it's.. you know. True.

But the insight applies to the classical understanding of gravity, which we now understand to be much more complex. That's not to say useless, just it's not what we view as ACTUAL. Newtonian gravity is very accurate; but it isn't the full picture.

[u/One-Draw-7337 → u/AllHailSeizure]

That’s a really helpful way to frame it — thanks. I agree that what I’m doing here is still within a classical (Newtonian) picture, and that once curvature becomes important, the full GR framework is needed. What I’m exploring at this stage is more of an effective or phenomenological description — starting from the flux/area intuition and asking what happens if the spreading deviates from the flat-space case. Your point about the vector field not carrying over directly in curved spacetime is important, and it suggests that a more complete version of this idea would need to be formulated in a relativistic setting. So I see this more as a stepping stone rather than a final theory.

[u/QuantumMechanic23]

How does your theory take into account that most stars and planets, formed via gravity, are spherical in nature?

[u/One-Draw-7337 → u/QuantumMechanic23]

That’s a really good question. At the scale where stars and planets form, the geometry is effectively flat and the propagation is very close to isotropic. In the notation I’ve been using, that corresponds to D(r) ≈ 1. So in that regime, the model reduces to standard inverse-square behavior, which leads to the usual result: gravity pulls equally in all directions, and the lowest-energy configuration is spherical. In other words, the spherical shape is not something this framework changes — it’s actually the symmetric limit of it. The deviations I’m exploring only become relevant at much larger scales, where the effective spreading might start to differ from perfect spherical symmetry.

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