For decades, scientists have faced a major mystery in astronomy. Galaxies contain stars, gas and dust that we can see, but these visible materials do not seem to provide enough gravity to explain how galaxies move.
Stars in the outer parts of galaxies often move much faster than expected. If only visible matter were present, many galaxies should not remain stable. Something appears to provide additional gravity.
Scientists usually explain this missing gravity using dark matter—an invisible form of matter that does not interact strongly with light but appears to affect ordinary matter through gravity.
However, observations have revealed another surprising clue. The amount of visible matter in a galaxy appears to be closely connected to the way the galaxy moves. This relationship is called the Radial Acceleration Relation, or RAR.
A new theoretical approach called Modified General Relativity (MGR) proposes that this relationship may have a deeper explanation involving the geometry of spacetime itself.
What Is the Radial Acceleration Relation?
Imagine looking at a galaxy from the outside.
Near the center, there are many stars and large amounts of gas. Farther away from the center, the amount of visible matter usually decreases.
According to ordinary Newtonian gravity, we would expect the gravitational pull to become weaker as we move farther away.
But observations show something unexpected.
Stars and gas in the outer regions of galaxies continue moving at surprisingly high speeds. Their observed gravitational acceleration is much greater than what we would calculate from visible matter alone.
This is one of the reasons scientists proposed the existence of dark matter.
But the story becomes even more interesting.
Researchers found that the observed acceleration is closely related to the acceleration produced by visible matter.
This relationship is extremely tight across many different galaxies.
That means the missing gravitational effect does not appear to be completely random.
Somehow, the visible matter and the additional gravitational effect seem to know about each other.
This mysterious connection is called the Radial Acceleration Relation.
Why Is the RAR Important?
The RAR is important because it raises a fundamental question:
Why should invisible dark matter follow such a close relationship with visible matter?
The standard cosmological model, called ΛCDM, explains galaxies using dark matter along with ordinary matter, dark energy and other components.
ΛCDM has been extremely successful in explaining many observations of the Universe.
However, the very tight RAR has encouraged scientists to investigate whether there could be a deeper explanation for the relationship between visible matter and gravity.
One alternative idea is called Modified Newtonian Dynamics, or MOND.
MOND suggests that Newton's laws of gravity may behave differently when gravitational acceleration becomes extremely weak.
MOND can successfully reproduce many galaxy rotation curves.
But according to the MGR proposal, MOND also has limitations.
For example, the acceleration scale used in MOND is normally treated as a fixed value. However, observations and theoretical analysis suggest that galaxies may not all behave in exactly the same way.
This creates an interesting possibility: perhaps MOND is capturing part of a deeper gravitational phenomenon rather than representing the complete theory.
What Is Modified General Relativity?
This is where Modified General Relativity, or MGR, enters the discussion.
MGR attempts to describe gravity and the mysterious dark sector using the geometry of spacetime.
Einstein's general relativity already tells us that gravity is closely connected to the shape and geometry of spacetime.
MGR extends this idea.
The theory introduces an additional mathematical object called Φαβ. In simple terms, this tensor is proposed to describe additional gravitational energy and momentum that are not completely represented by the standard Einstein equations.
According to the theory, this extra contribution can account for both dark energy and dark matter.
The Φ00 component is associated with the energy-related part of the dark sector and is used to describe dark energy.
The spatial components, written as Φij, are associated with stresses and are used to describe dark matter.
So instead of treating dark matter and dark energy as completely separate mysteries, MGR attempts to connect them through the structure of spacetime.
Could Dark Matter Be Part of Spacetime?
This is one of the most interesting ideas behind MGR.
In the standard picture, dark matter is generally considered to be some form of invisible matter or particle.
MGR takes a different approach.
It proposes that the dark sector is fundamentally connected to the Lorentzian geometry of spacetime.
The theory also describes dark matter using a spin-1 framework.
This could help explain why dark matter is so difficult to detect directly.
Scientists have searched for dark matter particles using underground detectors, space missions and particle experiments. So far, there has been no universally accepted direct detection of the dark matter particle.
If dark matter's gravitational behavior is deeply connected to spacetime geometry, its effects might be much easier to observe through gravity than through ordinary light or particle detectors.
How Could MGR Explain the RAR?
According to the MGR proposal, the RAR can arise naturally from a balance between different gravitational forces.
The outer parts of galaxies are particularly important.
Far from the galactic center, visible matter becomes less concentrated, but stars can still move at high speeds.
MGR proposes that the observed motion results from an interaction between the ordinary Newtonian gravitational force and forces associated with the dark sector.
In the inner regions of a galaxy, the balance between the different dark-sector contributions can be different.
The important result is that the total observed acceleration remains closely connected to the acceleration produced by ordinary matter.
This could provide a physical explanation for why the RAR is so tight.
In other words, the relationship between visible matter and galactic motion may not simply be a coincidence.
It could be a natural consequence of the underlying gravitational theory.
MGR and MOND
MGR does not necessarily treat MOND as completely wrong.
Instead, the theory claims that MOND-like behavior can appear as a particular limit of a more general gravitational framework.
This is an important difference.
MOND uses a characteristic acceleration scale, usually called a₀.
MGR allows quantities corresponding to parameters such as a₀ and γ to vary within its broader theoretical framework instead of requiring them to be universal fixed constants.
According to the MGR analysis, this makes the theory more flexible than MOND.
The idea is that MOND could describe part of what we observe in galaxies, while MGR attempts to explain why that behavior appears in the first place.
What About the Tully-Fisher Relation?
The RAR is also connected to another important relationship called the Tully-Fisher relation.
It connects the amount of ordinary matter in a galaxy with the speed at which the galaxy rotates.
A simple version of this relationship suggests that the baryonic mass is related to approximately the fourth power of rotational velocity.
However, MGR argues that the exact relationship does not have to be exactly the fourth power for every galaxy.
The result can depend on the shape of the galaxy's outer rotation curve.
Some rotation curves are nearly flat, while others continue rising or begin falling.
According to the MGR analysis, these differences can produce different effective exponents.
This could help explain why real galaxies do not all behave in exactly the same way.
Flat Rotation Curves Cannot Continue Forever
Another prediction of MGR concerns flat rotation curves.
Many galaxies show rotation curves that remain almost flat over large distances.
This means that stars far from the center continue moving at nearly similar speeds instead of slowing down as much as simple Newtonian calculations would suggest.
MGR argues that these flat curves should not continue forever.
Their length should depend on the amount of dark-sector contribution associated with the galaxy or galaxy cluster.
Therefore, galaxies with different amounts of dark matter should have different lengths of extended flat rotation curves.
What About Wide Binary Stars?
MGR also attempts to explain an unusual observation involving wide binary stars.
Wide binaries are pairs of stars separated by relatively large distances.
At such distances, their gravitational acceleration is very weak. Some studies have reported possible differences between their observed motions and what standard Newtonian calculations predict.
This has become an important topic in discussions about MOND and alternative theories of gravity.
According to the MGR proposal, the observed wide-binary anomaly can be explained without changing Newton's gravitational constant, G.
The theory also claims that an external gravitational field from other ordinary matter is not required for this explanation.
However, this remains an area where more observations and independent tests are needed.
Does MGR Replace Newtonian Gravity?
No.
One of the claims of MGR is that ordinary Newtonian gravity remains valid across a very wide range of scales.
This includes extremely large structures such as galaxy clusters.
Instead of completely replacing Newtonian gravity, MGR adds additional contributions associated with the dark sector.
This allows the theory to retain the familiar gravitational behavior that has been successfully tested in many situations.
The structure associated with Φ00, according to the theory, also provides an explanation for why Newtonian gravity emerges so naturally across the Universe.
A New Way to Think About Dark Matter
The Radial Acceleration Relation has created an important mystery.
Galaxies appear to follow a remarkably close relationship between their visible matter and their observed gravitational behavior.
The standard ΛCDM model explains this mainly through dark matter.
MOND attempts to explain it by changing the behavior of gravity at very low accelerations.
MGR offers a third possibility.
It suggests that dark matter, dark energy and gravity may all be connected to the geometry of spacetime.
According to the theory, the RAR could emerge naturally from the balance between ordinary gravitational forces and dark-sector effects.
MGR also attempts to explain MOND-like behavior, galaxy rotation curves, the Tully-Fisher relation and reported wide-binary anomalies while preserving Newtonian gravity on very large scales.
But it is important to remember that MGR is a theoretical proposal, not an established replacement for ΛCDM.
Its ultimate success will depend on whether future observations can distinguish its predictions from those of existing theories.
The biggest question remains open:
Is dark matter truly a new invisible substance—or could what we call dark matter be revealing something much deeper about the geometry of the Universe itself?
Reference: Gary Nash, "On the physical origin of the radial acceleration relation", Arxiv, 2026. https://arxiv.org/abs/2608.19245
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