GRAVITY IS LAZY

GRAVITY  IS  LAZY

— and that is why the universe looks the way it does —

JongJin Ma  ·  May 15 2026 

The universe has a preference

Look up on a clear night, far from city lights, and the first thing you notice is not the stars — it is the dark. The universe is mostly empty. What little matter exists has arranged itself into an extraordinary pattern: thin glowing threads of galaxies stretching across hundreds of millions of light-years, meeting at brilliant knots, surrounding vast dark voids that contain almost nothing.

This structure — called the cosmic web — is one of the most striking facts about our universe. It did not have to look like this. A ball of gas, if you set gravity running on it, would collapse into a sphere. So why threads? Why voids? Why this particular pattern across twelve orders of magnitude in physical scale?

The standard answer involves dark matter: hypothetical particles, never directly detected, which supposedly seeded the cosmic web by providing gravitational scaffolding for ordinary matter to fall into. 

This paper proposes something different. The cosmic web is not the result of a mysterious substance. It is the result of a principle — one that a child could state:

Gravity is lazy. It scatters flux in all directions by default. But when scattering becomes wasteful, structure emerges.

The economics of gravity

Imagine you need to deliver food to a hundred people spread across a large field. If the field is small and everyone is nearby, you can stand in the centre and hand food outward — simple, no organisation needed. 

But as the field grows, this strategy fails. Most of your effort goes to empty space. At some point it becomes cheaper to form a queue, or to build a distribution network.

Gravity faces exactly this problem. At small scales — inside the solar system, inside a globular cluster — the three-dimensional 'scatter' strategy works fine: the gravitational field radiates outward, reaches its targets, and the loss to empty space is negligible. But at the scale of a galaxy disk, something changes. The efficiency of 3D scattering drops as 1/r². At ten times the target distance, you reach only one-hundredth as much mass per unit flux. The waste is no longer negligible.

This is not a metaphor. It is the Gauss law of gravity: the total gravitational flux through any closed surface equals 4πGM, regardless of the surface's shape. Change the shape from a sphere to a cylinder — as happens when matter collapses into a disk — and the same total flux now passes through a much smaller effective area. The gravitational acceleration is stronger. The 'delivery' is more efficient.

The transition from 3D (spherical) to 2D (cylindrical) propagation occurs at a specific radius r₀, where the cost of scattering and the cost of restructuring break even. This break-even radius is, in a precise mathematical sense, the same as the transition radius identified from galaxy rotation curves: r₀ = k√M, where k encodes the universal surface density of galaxy disks (Freeman's Law, 1970). At r > r₀, it is cheaper to maintain a structured disk than to scatter isotropically. At r < r₀, scattering is fine. This single economic argument recovers the flat rotation curve, the Tully-Fisher relation (v⁴ ∝ M), and the critical acceleration a_crit = G/k² ≈ 8.6 × 10⁻¹⁰ m/s² — all without dark matter.

Why rotation exists

Here is a consequence of this lazy-gravity principle that I find beautiful. Flattening a non-rotating gas cloud into a disk costs energy: you have to suppress vertical motion, overcome thermal pressure, push material into the plane. This restructuring cost is real.

But a rotating cloud flattens automatically. Angular momentum conservation does the work for free. Once the cloud begins rotating — even slightly, from tidal interactions with neighbours — centrifugal force drives it into a disk at zero additional cost. And because angular momentum is conserved, the disk stays flat forever.

Rotation is not a by-product of galaxy formation. It is the universe's solution to a cost-minimisation problem.

Lazy gravity prefers rotation because rotation achieves 2D flux efficiency without paying the restructuring bill. The spiral arms that result are not decorative. They are the flux channels of the disk — the routes along which gravitational influence propagates most efficiently through the galaxy plane. Older galaxies have tighter arms because the channels have deepened over time, exactly as old rivers carve deeper valleys.

Clusters, hubs, and the Steiner tree

At galactic scales, the lazy-gravity principle drives matter into disks via the feedback mechanism (the details of which are the core of this research programme). But the same economics operate at much larger scales, with a crucial difference: at cosmological scales, the transition to 1D propagation becomes economic.

In a 1D filament — a thread of galaxies — the gravitational field does not dilute with distance at all. The effective area A_eff is constant: proportional to the cross-section H², independent of distance along the filament. Delivery efficiency is perfect. The cost of building a filament is high, but once built, it pays indefinitely.

Galaxy clusters sit at the intersections of these filaments. They are not simply large concentrations of matter; they are hubs in a gravitational delivery network. Each connecting filament brings flux from a different direction, and at the hub those fluxes converge. With n filaments connecting to a cluster, the effective gravitational acceleration is g = n·GM/(4πHr) — n times stronger than Newton predicts from the baryonic mass alone. The 'dark matter' in clusters is the mathematical shadow of this hub geometry.

Remarkably, this network — filaments connecting clusters — is mathematically equivalent to a Steiner minimum tree: the network of minimum total length that connects a given set of nodes, possibly through intermediate junction points. The Steiner tree has two known mathematical properties that match cosmic observations precisely:

120° junction angles — Steiner trees always branch at 120° to minimise total length. Filaments in the cosmic web preferentially meet at this angle.

Maximum node degree ≈ 6 — in 3D, Steiner trees cannot branch into more than 6 edges at a point. Observed cluster filament connectivity: n ≈ 6.

The Steiner minimum tree problem is NP-Hard: no computer algorithm solves it efficiently. But the universe solves it constantly, at every point in space, using the greedy local algorithm of gravitational feedback: flux always flows toward the steepest gradient. The cosmic web is the universe's approximate solution to an NP-Hard optimisation problem, computed by physics in parallel across all of space.

Isotropic gravity cannot build a directed network. Feedback-modified gravity — where the propagation geometry depends on the matter structure that feedback itself created — can and must.

What dark matter really is

In this framework, the distribution of 'dark matter' is not a map of an invisible substance. It is a map of gravitational flux transport infrastructure:

No dark matter — Newton is exact. The galaxy or system is small enough that 3D scattering is still efficient, or isolated enough that no external channels exist. Example: NGC 7507, small isolated ellipticals.

Spherical NFW halo — the galaxy has built its own radial flux channels through radially-biased stellar orbits (velocity anisotropy β > 0). The NFW profile's three zones correspond to Newton core, transition zone, and channel attenuation. Example: massive isolated ellipticals such as NGC 4555.

Elongated halo aligned with filament — the galaxy is embedded in the cosmic web and uses pre-built filamentary channels at zero additional cost. Example: BCGs in rich clusters.

The NFW profile — the universal dark matter halo shape fitted to thousands of systems — has been derived numerically from N-body simulations for fifty years. In this framework, it emerges analytically: inner 1/r from the Newtonian core, middle 1/r² from the spherical-to-cylindrical transition, outer 1/r³ from channel attenuation. No simulation required. No dark matter required.

A prediction

This framework makes a sharp, testable prediction: the apparent dark matter fraction of a galaxy should correlate with its infrastructure strategy, not its mass alone. Two galaxies of the same mass but different environments — one isolated, one embedded in a cluster with n = 6 filaments — should show dark matter fractions differing by a factor of n. Euclid weak lensing data, cross-matched with cosmic web filament catalogues from DESI, will test this directly.

A further prediction: massive isolated ellipticals that built their own radial channels (Strategy B2) should show radially anisotropic stellar kinematics (β > 0) and spherical dark halos. Cluster BCGs that borrowed external filamentary channels (Strategy A) should show isotropic kinematics (β ≈ 0) and halos elongated toward the filament axis. This distinction is measurable with MUSE and WEAVE integral-field spectroscopy.

The critical test for the counter-example that keeps me honest: NGC 4555, an apparently isolated giant elliptical with a large dark halo. Strategy B2 predicts β > 0 and a spherical halo. If instead the kinematics show β ≈ 0 and the halo is elongated toward a filament, the galaxy was never truly isolated — and Strategy A applies. Either outcome is falsifiable.

This post summarises theoretical work in progress. The full technical paper (v3.12) is available on Zenodo. Comments and criticism are welcome.

Keywords: gravitational feedback · cosmic web · dark matter · Tully-Fisher · Steiner tree · delivery efficiency · Freeman's Law