Black holes are among the most mysterious objects in the universe. They are famous for their incredibly strong gravity, which is so powerful that not even light can escape once it crosses the event horizon. Wormholes are even more mysterious. They are theoretical tunnels that could connect two different places in space or even different moments in time. While wormholes have never been observed, they are allowed by some solutions of Einstein's theory of gravity.
Now, a new study by Chandra and Post looks at black holes and wormholes from a completely different perspective. Instead of asking how massive they are or how they pull on nearby objects, the researchers asked a simple question:
What happens if we slightly change their shape or the way their mass is distributed?
Their answer reveals that some black holes and wormholes behave a little like elastic objects. They are not made of rubber or metal, but they can still resist small changes in a measurable way. This surprising idea gives scientists a new tool for understanding gravity, quantum physics, and the hidden structure of black holes.
A Different Kind of Black Hole
The researchers studied a special type of black hole called a thin-shell black hole. In this model, all the matter is concentrated on a very thin layer called a shell. They also studied thin-shell wormholes, which are built in a similar way.
The team imagined making tiny changes to this shell. For example, they slightly changed its shape or moved a little mass from one part of the shell to another. Then they calculated how the whole gravitational system reacted.
This may sound like a small change, but it can reveal a lot about how black holes work.
Measuring How "Stiff" a Black Hole Is
To describe the response, the researchers introduced something called a stiffness kernel.
Don't let the name scare you. The idea is actually simple.
Imagine pressing on a mattress. A soft mattress bends easily, while a firm mattress pushes back more strongly. That resistance tells you how stiff the mattress is.
The same idea can be applied mathematically to black holes.
The stiffness kernel measures how strongly a black hole or wormhole resists small changes in its shape or mass distribution.
A larger response means the object is harder to deform. A smaller response means it changes more easily.
Although black holes are not physical objects you can touch, this mathematical idea helps scientists understand how stable they are.
Two Ways to Change the Shell
The researchers looked at two kinds of changes.
The first was changing the shape of the shell. Imagine gently pushing on different parts of the shell so it becomes slightly uneven.
The second was changing the mass density. Instead of changing the shape, they imagined adding a tiny bit of mass to one part of the shell and removing the same amount somewhere else.
Both changes affect the gravitational field, but in different ways.
By studying these responses, the scientists learned more about the hidden properties of black holes and wormholes.
A Connection to Quantum Physics
One of the most exciting parts of the study is that the same calculations also describe something in quantum physics.
According to a famous idea called the AdS/CFT correspondence, some gravitational systems have an equivalent description using quantum field theory.
In this quantum picture, the thin shell behaves like a line defect. You can think of a line defect as a special line inside a quantum system where the physical properties are different from the surrounding area.
When the shell changes shape or mass, the line defect changes too.
This means the same mathematical equations describe both gravity and quantum physics at the same time.
That is one reason why this research is so important.
Special Mathematical Tools
The researchers identified two important mathematical quantities.
The first is called the displacement operator. It measures what happens when the shell changes shape.
The second is the mass-density operator. It measures what happens when the amount of mass changes at different points along the shell.
Together, these two quantities explain how the shell responds to different kinds of disturbances.
Although these names sound technical, they simply help scientists describe two different ways a black hole can react.
Not Every Black Hole Behaves the Same
One of the most interesting discoveries is that different black holes can behave in different ways.
The researchers found that the possible vibrations of the shell depend on the surrounding geometry.
In some cases, only certain vibration patterns are allowed. This is called a discrete spectrum.
In other cases, there is a continuous range of possible vibrations. This is called a continuous spectrum.
This difference completely changes how the system behaves over time.
When Disturbances Fade Away
Imagine dropping a stone into a calm pond.
The ripples spread outward and slowly disappear.
Something similar can happen with thin-shell black holes.
If the shell has a continuous spectrum, a small disturbance gradually fades away.
The energy spreads into the surrounding space, and the shell slowly returns to its original state.
Scientists call this process relaxation.
It is similar to how vibrations in a bell eventually disappear after it is struck.
When Vibrations Never Stop
Things are different when the shell has a discrete spectrum.
Instead of fading away, the vibrations keep repeating.
The energy cannot escape, so the shell continues oscillating.
This is similar to a musical instrument producing a standing wave that continues for a long time.
Whether the vibrations disappear or continue forever depends on the geometry around the shell.
This was one of the most important findings of the study.
A Link Between Three Areas of Science
The researchers found that their work connects three different branches of physics and mathematics.
The first is gravity, because they are studying black holes and wormholes.
The second is quantum physics, because the same system can also be described using quantum field theory.
The third is geometry, because understanding the shell requires studying curved mathematical surfaces.
Usually these subjects are studied separately.
This research shows that they are actually closely connected.
The same mathematical tools can describe all three at once.
Understanding Black Hole Information
The study also explores what these elastic changes mean for black hole entropy.
Entropy is a measure of how many microscopic arrangements can create the same black hole.
Many physicists believe understanding entropy is the key to solving one of the biggest mysteries in modern science—the black hole information problem.
The researchers found that changing the shape and mass of the shell affects these microscopic states.
This suggests that elastic deformations could play an important role in how black holes store information.
Although much more work is needed, this idea may help scientists better understand the quantum nature of black holes.
Why This Research Is Important
This study does not suggest that black holes are soft objects that can be stretched like rubber.
Instead, it shows that they have mathematical properties similar to elasticity.
By measuring how black holes respond to tiny changes, scientists can learn more about their stability, their internal structure, and their connection to quantum physics.
The work also introduces a new way to study how disturbances disappear over time and how black holes may encode information.
Perhaps most importantly, it brings together gravity, quantum theory, and geometry into a single framework.
Although the mathematics behind the study is highly advanced, the main idea is surprisingly simple: even tiny changes in the shape or mass of a black hole can reveal hidden properties that were previously impossible to see.
As researchers continue exploring these ideas, they may move one step closer to answering some of the biggest questions about the universe, including how gravity and quantum physics fit together and what really happens inside a black hole.
Reference: Jeevan Chandra, Boris Post, "Elastic stiffness of three-dimensional black holes and wormholes from Liouville line defects", Arxiv, 2026. https://arxiv.org/abs/2607.16155
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