Wormholes are among the strangest and most fascinating ideas in modern physics. They are theoretical tunnels through spacetime that could connect two very distant places in the Universe. Instead of traveling the normal distance between those places, a traveler could, in theory, pass through a wormhole and reach the other side much faster.
But there is a major problem: keeping a wormhole open may require a very unusual type of matter.
A new theoretical study by Remo Garattini and his team looks at this problem from a different angle. The researchers studied whether a special type of matter described by a polytropic equation of state could support traversable wormholes.
Their work does not mean that humans can build a wormhole today. Instead, it gives physicists a new mathematical way to study what kind of matter and spacetime structure might be needed to keep one open.
What exactly is a wormhole?
A wormhole can be imagined as a shortcut through spacetime.
Think of a sheet of paper with two points drawn far apart. Normally, you would have to travel across the sheet from one point to the other. But if you fold the paper so the two points come close together and create a tunnel between them, the distance through the tunnel becomes much shorter.
A wormhole is somewhat similar, except that the "sheet" is spacetime itself.
Einstein's theory of general relativity allows mathematical solutions that look like wormholes. However, not every wormhole would be possible to travel through.
A traversable wormhole must have a throat that stays open long enough for something to pass through it.
And this is where the biggest problem begins.
The problem with keeping a wormhole open
Gravity normally pulls matter together. Because of this, a wormhole throat would tend to collapse unless something prevents it.
According to general relativity, keeping the throat open requires the geometry of spacetime to satisfy something called the flare-out condition.
This condition has an important consequence.
The matter around the throat must violate the null energy condition, or NEC.
In simple terms, the NEC is a condition that describes how matter and energy should behave when they interact with gravity and light-like paths. Ordinary matter generally satisfies it.
Wormholes, however, need something different.
This unusual material is often called exotic matter.
Scientists have considered many possible forms of exotic matter, including phantom-like energy and unusual fluids. Garattini and his team investigated another possibility: matter described using a polytropic equation of state.
What is a polytropic equation?
A polytropic equation of state is simply a mathematical relationship between the pressure and density of matter.
It is not something invented specifically for wormholes. Polytropic models are already used in astrophysics to describe objects such as stars and other compact objects.
One reason they are useful is that a small number of parameters can describe different physical conditions.
The researchers wanted to see what would happen if this type of matter were used to support a wormhole.
They studied two main cases: homogeneous and inhomogeneous matter.
The simple case: homogeneous matter
In the homogeneous model, the important properties of the matter remain constant throughout the wormhole.
The researchers used these constant parameters to calculate the density, pressure and shape of the wormhole.
They found mathematical solutions that can describe a wormhole interior.
However, these wormholes generally do not extend forever into space. Instead, the wormhole interior has a finite size.
This is actually an interesting feature.
Rather than requiring exotic matter to fill an unlimited region, the wormhole could exist inside a limited area and then be connected to an ordinary vacuum region outside it.
In other words, the strange matter could potentially be restricted to the wormhole's interior.
A more flexible model
The researchers then considered a more interesting possibility.
What if the properties of the matter changed depending on how far you are from the wormhole's center?
To describe this, they allowed the polytropic coefficient to become a function of distance, written as ω(r).
This creates an inhomogeneous wormhole.
The idea is quite simple: instead of having the same type of matter everywhere, its properties can change from one location to another.
This gives the researchers much more freedom.
In fact, their calculations show that once the function ω(r) is chosen, the resulting wormhole geometry can be determined.
So there is a direct relationship between the way the exotic matter is distributed and the shape of spacetime around it.
Different matter distributions create different wormholes
To explore this idea, the researchers used a power-law profile for the radial dependence of the polytropic coefficient.
This allowed them to create several different mathematical wormhole solutions.
Depending on the values of the parameters, the solutions can have different shapes. Some produce power-law behavior, while others lead to logarithmic forms.
An important result is that several of these solutions have finite radial support.
That means the unusual matter and wormhole geometry can be restricted to a limited region.
Beyond that region, the wormhole interior could potentially be connected to an exterior vacuum solution.
This is interesting because it offers a possible way to keep the exotic matter localized rather than spreading it throughout a huge area.
A surprising wormhole appears
One of the most interesting results occurs for a special relationship between two parameters:
α = 2γ − 3
Under this condition, the equations naturally produce a configuration similar to what is known as a generalized absurdly benign traversable wormhole, or GABTW.
Despite its strange name, the basic idea is easy to understand.
The goal of an "absurdly benign" wormhole is to keep the unusual matter and the complicated spacetime geometry confined to a relatively small region.
In the solution studied by the researchers, the wormhole ends at a finite distance. Under the assumptions of their model, it can then be connected to a flat exterior region.
What makes this especially interesting is that the GABTW-like configuration was not simply assumed at the beginning. It naturally appeared from a particular choice of the inhomogeneous polytropic matter.
The exotic matter problem is not completely solved
It is important not to misunderstand the result.
The researchers did not eliminate the need for exotic matter.
The wormhole throat still violates the null energy condition, as expected from the flare-out requirement in general relativity.
However, the inhomogeneous model provides something useful: control over where the violation occurs and how it changes with distance.
This means researchers can study configurations in which the exotic behavior is concentrated around the throat instead of being spread across a much larger region.
For some solutions, the total amount of matter violating the averaged null energy condition can remain finite. With suitable parameter choices, the amount near the throat can also be reduced.
That makes these mathematical solutions interesting for further research.
Could a person actually travel through one?
The study also looks at some conditions related to traversability.
For the particular constant-redshift configuration studied, a traveler would not experience acceleration caused by the redshift function. The researchers also examine tidal forces, which describe how strongly gravity could stretch or compress a traveler.
The radial tidal-force requirement can be satisfied under the model's assumptions.
However, sideways or lateral tidal forces place limits on the travel speed.
So even if the mathematics allows a traversable wormhole, that does not mean it would automatically be safe for a human.
What does this research really mean?
This research is still entirely theoretical.
There is currently no experimental evidence showing that naturally occurring traversable wormholes exist. Scientists also do not know whether the required exotic matter can actually exist in the necessary form or quantity.
The importance of this work is that it provides a new mathematical framework for studying the relationship between matter and wormhole geometry.
The homogeneous model shows what happens when the properties of the matter remain constant.
The inhomogeneous model is more flexible because the properties of the matter can change with distance.
This produces a much larger variety of possible wormhole structures.
What could scientists study next?
There are many possibilities for future research.
Scientists could investigate wormholes with more complicated redshift functions instead of assuming a constant one. They could also test different ways of changing the polytropic properties with distance.
Another important step would be connecting these wormhole interiors directly to known exterior solutions, such as a Schwarzschild vacuum, and then studying whether the combined structure remains stable.
Researchers could also investigate rotating or time-dependent wormholes.
Most importantly, they need to study stability.
A mathematical solution may satisfy Einstein's equations but still collapse when exposed to a small disturbance. Understanding whether these wormholes can survive such disturbances is essential.
A new perspective on wormholes
The main contribution of this research is not the discovery of a real wormhole. Instead, it shows that the properties of exotic matter can be closely connected to the geometry of a wormhole.
By using a polytropic equation of state, especially one that changes with distance, researchers can create and study many different wormhole configurations.
Some of these solutions can have a finite size, while a special choice of parameters produces a GABTW-like configuration in which the unusual matter can be concentrated within a limited region.
For now, traversable wormholes remain theoretical possibilities. But research like this helps scientists understand what the Universe would need to allow such extraordinary structures—and just how unusual the required matter may have to be.
Reference: Remo Garattini, Emmanuel N. Saridakis, Athanasios G. Tzikas, "Polytropic wormholes", Arxiv, 2026. https://arxiv.org/abs/2608.16969
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