How Weak Gravity Does Without Dark Matter ⚡ экспресс

Original: "A Relativistic MOND"

arXiv:2601.04290v1 · 2026-01-07 · CC BY · ⏱ 1 min · General Relativity Cosmology Galaxies

Scientists have found a way to explain galaxy rotation by changing the law of gravity on the outskirts—no dark matter required.

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Astronomers, including Vera Rubin, noticed that stars on the outskirts of galaxies rotate faster than visible mass allows. To explain this, they invented dark matter—an invisible ballast. But there's another possibility: gravity isn't always the same. In a very weak field, like on the galactic fringes, it changes character—like a sound that's deafening up close but turns into a whisper far away.

The MOND theory, proposed by Jacob Bekenstein and Mordehai Milgrom, describes this change, but for a long time it didn't mesh with Einstein's picture of curved spacetime. Now physicists have found a way to reconcile them: they add a tiny correction to the equation of spacetime curvature, one that only kicks in at accelerations hundreds of billions of times weaker than Earth's gravity. Remarkably, the threshold of this 'whisper' is set by the expansion of the universe: it matches the size of its visible part—the horizon from which light reaches us.

At the limit of the weakest gravity, the equations gain scale invariance: double all distances, and nothing changes. It's as if space at these frontiers has no preferred ruler.

🎯 The critical acceleration at which gravity changes its behavior is about a hundred billion times smaller than what we feel on Earth. That's like the difference between a thunderclap and the flutter of a butterfly's wing.

a_0 = \frac{c^2}{\xi \ell_{\rm dS}}

a0 — critical acceleration, c — speed of light, ℓ_dS — de Sitter radius (characteristic size of the universe), ξ — a number close to one.

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How Weak Gravity Does Without Dark Matter ⚡ экспресс