Imagine a universe where black holes—those cosmic monsters known for their inescapable pull—could repel each other instead of attracting.
Sounds impossible, right?
Yet, a new theoretical study by physicists Li, Liu, and Lu has done exactly that—by constructing a new class of black holes using what’s called the curvature-induced scalarization mechanism in Einstein’s theory of gravity. Their work reveals that black holes can emerge from the same kind of “exotic matter” that makes wormholes possible—bridges that could theoretically connect distant parts of space and time.
This discovery challenges one of the oldest assumptions in physics: that black holes always attract. Instead, depending on how they are formed, they might actually push each other away, or even possess negative mass—a concept that turns our traditional understanding of gravity upside down.
A Century-Old Mystery Revisited
To understand how revolutionary this idea is, let’s go back to the early 20th century.
In 1916, Albert Einstein published his General Theory of Relativity, forever changing the way we view space, time, and gravity. That same year, physicist Karl Schwarzschild discovered the first mathematical solution to Einstein’s equations—what we now know as the Schwarzschild black hole.
But around the same time, another strange solution appeared in the equations: the wormhole, a theoretical “tunnel” through spacetime that could link two distant regions of the universe.
For decades, scientists debated whether wormholes could exist. The problem was that creating or maintaining a wormhole seemed to require “exotic matter”—a substance that violates the so-called null energy condition, meaning it behaves in ways that normal matter never could. Ordinary matter collapses under gravity, but exotic matter could resist or even reverse gravitational pull.
Because no known substance behaves this way, wormholes were long considered pure speculation—beautiful mathematics without physical reality.
Phantom Matter: The Exotic Ingredient
Then came a new idea: phantom fields or phantom matter.
In modern cosmology, scientists use “phantom energy” to explain why the expansion of the universe seems to be accelerating. This form of energy acts as if it has negative pressure, pushing space apart instead of pulling it together.
Phantom matter, in essence, is the opposite of normal matter. Instead of attracting, it can repel. Instead of gaining energy when compressed, it loses it. It’s strange, unstable, and—until recently—wasn’t taken very seriously.
But recent developments in high-precision cosmology, combined with progress in string theory and the AdS/CFT correspondence, have brought phantom fields back into the spotlight. Some researchers even argue that phantom fields might be essential for understanding dark energy—the mysterious force making the universe expand faster and faster.
Li, Liu, and Lu wondered:
If exotic phantom matter can create stable wormholes, could it also produce new kinds of black holes?
From Wormholes to Black Holes
In Einstein’s gravity, there are exact mathematical solutions describing spherically symmetric, static universes coupled to a massless scalar field—a simple field that spreads out evenly through space. These solutions are defined by two parameters:
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M – the mass of the object, and
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Σ (Sigma) – the “scalar charge,” which represents the strength of the scalar field or “scalar hair.”
Normally, black holes are not allowed to have such “hair” (extra parameters) according to the famous no-hair theorem—they can only be described by mass, charge, and spin. But phantom fields change the game.
When the scalar field is phantom-like—meaning its energy behaves oppositely to normal energy—the equations allow new kinds of wormholes to exist. One of the best-known examples is the Ellis wormhole, discovered in the 1970s. It’s a smooth, stable passage connecting two universes, made possible by phantom energy.
These wormholes can have different combinations of M and Σ. When Σ > M, the wormhole is stable and repulsive—two such wormholes actually push each other away at long distances.
Li, Liu, and Lu extended this logic to black holes. They used the curvature-induced scalarization mechanism to “convert” or descalarize wormholes into black holes—essentially stripping away their independent scalar charge until it becomes a secondary effect of their mass.
The Curvature-Induced Scalarization Mechanism
This mechanism sounds complex, but the idea is elegant.
In physics, “scalarization” means giving an object an additional scalar field—an invisible quantity that changes how it interacts with space and time. The process is “curvature-induced” because it happens when spacetime curvature (how space bends due to gravity) interacts with the scalar field through a special term known as the Gauss-Bonnet term.
This term appears in advanced versions of Einstein’s gravity—like those inspired by string theory—and modifies how the scalar field behaves around massive objects like black holes.
When the scalar field becomes unstable around a Schwarzschild black hole (the simplest type), the system undergoes scalarization—a new black hole forms, now with “scalar hair.”
Li, Liu, and Lu applied this same process to phantom scalar fields, creating what they call phantom scalarized black holes.
Surprisingly, the equations allowed for negative-mass black holes and even black holes that repel each other depending on the ratio between mass and scalar charge.
When Black Holes Repel
In classical physics, two masses always attract through gravity.
But in this new framework, the long-range force between two identical black holes is given by a simple equation:
[
F \propto -M^2 - \epsilon \Sigma^2
]
Here,
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ε = +1 for normal scalar fields,
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ε = -1 for phantom scalar fields.
This means that if the black hole’s “phantom hair” (Σ) is large enough, the total force can flip sign—turning attraction into repulsion.
In other words, two phantom black holes can push each other away rather than pull together.
This result is astonishing because it suggests that gravity—traditionally thought to be purely attractive—could become repulsive under the influence of exotic matter.
It also implies that black holes could behave like particles with charge—sometimes attracting, sometimes repelling, depending on their internal properties.
Negative-Mass Black Holes: Breaking the Rules
Even more shocking, Li, Liu, and Lu’s equations show that phantom scalarized black holes can have negative mass.
In everyday physics, mass is always positive—it’s what gives matter its gravitational pull. Negative mass, if it existed, would behave in bizarre ways: push things it’s attracted to, move opposite to the direction of applied force, and create runaway effects if paired with positive mass.
Negative-mass black holes challenge nearly every intuition we have about spacetime, but they arise naturally in this model when phantom matter dominates.
While there’s no experimental evidence for such objects, their theoretical existence suggests that the universe might allow much stranger configurations of energy and gravity than we currently imagine.
Descalarization: When Wormholes Become Black Holes
Perhaps the most poetic part of the study is the dual nature of the process.
From the black hole’s perspective, the curvature-induced scalarization adds new “hair” to the black hole.
But from the wormhole’s perspective, the same mechanism acts as descalarization—removing its independent scalar charge and transforming it into a black hole.
In essence, a wormhole filled with phantom energy can collapse into a black hole whose properties are determined solely by its mass.
This means that the boundary between wormholes and black holes may not be as sharp as we once thought—they could simply be two sides of the same cosmic coin, connected by the behavior of the phantom field.
Why This Matters for Modern Physics
This research isn’t just a mathematical curiosity—it carries deep implications for our understanding of gravity, spacetime, and the limits of Einstein’s theory.
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It connects wormholes and black holes
Traditionally, wormholes required exotic matter, while black holes did not. This new work shows that the same exotic matter responsible for wormholes can also create new classes of black holes—blurring the line between these two extreme cosmic objects. -
It challenges the no-hair theorem
The theorem says black holes can’t have independent scalar fields. But curvature-induced scalarization violates this rule in a controlled, predictable way—allowing new types of black holes with measurable scalar “signatures.” -
It introduces repulsive gravity and negative mass
These phenomena are rare in classical physics, but common in theories involving phantom fields. If such effects could ever be observed, they might reveal the presence of exotic matter or even new dimensions of spacetime. -
It supports extensions of General Relativity
The Gauss-Bonnet coupling used in the model naturally arises in string theory and higher-dimensional physics. This suggests that phantom scalarized black holes might be windows into deeper layers of reality beyond Einstein’s equations.
How Could We Detect Such Black Holes?
While purely theoretical for now, these phantom black holes might leave detectable clues. For example:
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Gravitational waves from colliding black holes could carry unique “fingerprints” if one or both have scalar hair.
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Black hole shadows, like the one imaged by the Event Horizon Telescope, could appear distorted or asymmetrical.
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Cosmic repulsion effects in certain regions might hint at phantom fields affecting local gravity.
Future observatories and gravitational wave detectors—such as LISA and Einstein Telescope—could, in principle, test some of these predictions.
A Universe of Possibilities
Li, Liu, and Lu’s findings reveal something profound:
The universe might be far stranger than the black-and-white picture painted by standard general relativity.
If phantom matter truly exists, then black holes could have repulsive gravity, negative mass, or even evolve from wormholes. Exotic matter, once dismissed as science fiction, could be the key to understanding the most mysterious structures in the cosmos.
This work doesn’t just redefine what black holes are—it redefines what gravity itself can be.
The study reminds us that even after a century of Einstein’s theory, spacetime still holds secrets we are only beginning to uncover.
In Simple Terms
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Wormholes are tunnels through space, needing “exotic” matter to stay open.
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Phantom matter is one kind of exotic matter that can make wormholes stable.
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Li, Liu, and Lu used phantom matter and Einstein’s gravity to build new black holes with strange properties.
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These black holes can repel each other, or even have negative mass.
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The process that forms them turns wormholes into black holes—a kind of cosmic transformation.
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Their study shows that gravity, far from being just attractive, can act in surprising new ways when phantom matter is involved.
Conclusion: When the Universe Defies Intuition
For decades, black holes were seen as the ultimate “point of no return”—the cosmic vacuum cleaners from which nothing escapes.
But Li, Liu, and Lu’s research suggests a new narrative: in the deep mathematics of spacetime, black holes can behave like wormholes, repel each other, and even carry negative mass.
It’s a thrilling reminder that the cosmos doesn’t always follow our expectations.
Sometimes, it bends the rules of reality itself.
The frontier of physics is expanding—not just outward into the stars, but inward, into the very equations that define existence.
And as this study shows, even the darkest regions of the universe might still have a few bright surprises left to reveal.
Reference: Ze Li, Hai-Shan Liu, H. Lu, "Desclarizing the Wormhole to Black Hole with Negative Mass", Arxiv, 2025. https://arxiv.org/abs/2509.20755
Technical Terms
🌀 1. Einstein’s General Theory of Relativity
This is the theory Albert Einstein proposed in 1915.
It says that gravity is not a force, but the bending (curving) of space and time caused by mass and energy.
For example, the Sun bends space around it, and that’s why planets move in orbits — not because they’re “pulled” by a force, but because they’re following curved space.
⚫ 2. Black Hole
A black hole is a region in space where gravity is so strong that nothing—not even light—can escape.
It forms when a very massive star collapses under its own gravity.
We can’t see black holes directly, but we can detect their effects on nearby stars and light.
🕳️ 3. Wormhole
A wormhole is a theoretical tunnel that could connect two different places in space (or even time).
Imagine folding a piece of paper so two distant points touch — a wormhole is like a shortcut through space that does the same thing.
However, wormholes need “exotic matter” to stay open, which doesn’t exist naturally (at least not yet discovered).
🧪 4. Exotic Matter
This is a kind of matter that behaves opposite to normal matter.
Normal matter attracts; exotic matter can repel or counteract gravity.
It has unusual energy properties, like negative energy density, which violates normal physical rules.
Scientists think such matter could make wormholes possible.
👻 5. Phantom Matter (or Phantom Field)
This is a special type of exotic matter.
Instead of pulling things inward with gravity, phantom matter pushes things away.
It has “negative pressure” and might explain why our universe’s expansion is speeding up.
In simple terms — phantom matter acts like anti-gravity energy.
🧲 6. Scalar Field
A scalar field is like a number assigned to every point in space, representing some physical quantity (like temperature or energy).
It doesn’t have direction, only value.
In this article, the scalar field interacts with gravity and helps form wormholes or black holes.
Example:
If you imagine space as a 3D map, a scalar field is like writing one number (say, temperature) at every point on the map.
🧠 7. Scalar Hair / Scalar Charge (Σ)
In physics, “hair” is a nickname for extra properties that describe a black hole beyond its mass, charge, and spin.
A “scalar hair” means the black hole has an extra layer of information — like a field surrounding it.
The symbol Σ (Sigma) represents how strong that scalar field is.
Usually, according to the no-hair theorem, black holes aren’t supposed to have this.
But in the new study, they do, because of phantom fields.
🚫 8. No-Hair Theorem
This rule says:
“All black holes are simple. They can be fully described by just three numbers — their mass, electric charge, and spin (rotation).”
They can’t have other properties like scalar fields (hair).
But Li, Liu, and Lu’s work shows that under certain conditions, this rule can be broken, and black holes can have “extra features.”
🧭 9. Gauss–Bonnet Term
This is a special mathematical term that appears in advanced versions of Einstein’s gravity.
It connects spacetime curvature (how space bends) to energy and fields (like scalar fields).
Adding this term changes how gravity behaves at very high energies — for example, near black holes.
It comes from string theory and helps explain the “curvature-induced scalarization” mentioned in the paper.
⚙️ 10. Curvature-Induced Scalarization
This long phrase means:
When space is curved strongly (like near a black hole), it can trigger the growth of a scalar field — giving the black hole “hair.”
So, the bending of space itself creates or induces this extra field.
It’s like space “activating” new properties in the black hole when conditions are right.
🌀 11. Scalarization vs. Descalarization
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Scalarization: A process where a black hole gains scalar hair (it gets an extra property).
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Descalarization: The reverse — the object loses its independent scalar field and becomes simpler.
In the article, wormholes descalarize into black holes, meaning they lose their independent scalar charge Σ.
⚖️ 12. Phantom Scalar-Hairy Black Hole
This is a black hole that’s surrounded by a phantom scalar field — meaning it’s made partly from exotic matter that behaves oppositely to normal matter.
Because of that, these black holes can have unusual features like repulsive gravity or even negative mass.
💥 13. Negative Mass
This sounds strange, but mathematically it means a black hole (or object) that behaves in reverse to normal gravity.
If you push it, it moves toward you instead of away.
If placed near a positive mass, it could create bizarre runaway effects.
Negative mass isn’t known to exist, but it can appear in theoretical models like the one discussed.
🧮 14. Long-Range Force
This means the force that acts even when objects are very far apart — like gravity or electromagnetism.
In normal black holes, this force is always attractive.
But in phantom black holes, the long-range force can be attractive, neutral, or repulsive, depending on the balance between mass (M) and scalar charge (Σ).
🌌 15. Schwarzschild Black Hole
This is the simplest kind of black hole — non-rotating, uncharged, and perfectly spherical.
It’s often used as the “standard model” black hole in relativity because it’s easy to describe mathematically.
Li, Liu, and Lu compare their new phantom black holes to the Schwarzschild one.
💫 16. Ellis or Ellis–Bronnikov Wormhole
This is a specific type of traversable wormhole (you could, in theory, travel through it).
It’s supported by phantom energy instead of normal matter.
It connects two universes or two distant points in one universe and doesn’t collapse immediately like normal wormholes would.
🧱 17. Einstein–Scalar–Gauss–Bonnet (ESGB) Gravity
This is a modified version of Einstein’s gravity that includes both:
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a scalar field, and
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the Gauss–Bonnet term.
It allows new types of black holes with scalar hair to exist — something not possible in plain General Relativity.
🧱 18. Einstein–Phantom–Scalar–Gauss–Bonnet (EPSGB) Gravity
This is like ESGB gravity but uses a phantom scalar field (with opposite sign).
This version allows even stranger results — such as black holes with negative mass and repulsive interactions.
🧩 19. Asymptotically Flat Spacetime
This means that far away from a black hole or wormhole, space becomes flat and behaves normally — like the space we live in.
In other words, the effects of gravity disappear at large distances.
🧭 20. Instability
In physics, instability means a small disturbance can grow uncontrollably.
In this case, when a scalar field becomes unstable near a black hole, it causes the black hole to change — triggering scalarization and forming a new kind of black hole.
✅ In Short:
| Term | Simple Meaning |
|---|---|
| Wormhole | Tunnel connecting two parts of space. |
| Phantom Matter | Exotic matter that acts like anti-gravity. |
| Scalar Field | A value that fills space and affects gravity. |
| Scalar Hair (Σ) | Extra property of a black hole from a scalar field. |
| Curvature-Induced Scalarization | When space bending creates new fields. |
| Descalarization | When a wormhole becomes a black hole. |
| Negative Mass | Mass that causes repulsive gravity. |
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