Black holes are some of the strangest and most powerful things in the universe. They are places where gravity is so strong that nothing—not even light—can escape. For years, scientists believed we understood how they work. But now, a new study has used a special kind of math to show that black holes might be very different from what we thought.
This new math is called fractional calculus, and it has helped scientists discover a new kind of black hole—one that is not smooth and round like a ball, but fractal like a snowflake or a jagged coastline. Even stranger, these black holes are colder, more complex, and don’t follow the usual rules of space and time.
Let’s break this down and see how this changes everything we knew about black holes.
๐ What is a Black Hole?
A black hole is formed when a very big star collapses. All of its mass gets squeezed into a very small space, creating a strong pull of gravity. Around the black hole is something called an event horizon—a kind of invisible surface. Once something crosses it, it can never come back.
In 1974, famous scientist Stephen Hawking shocked the world by saying that black holes are not completely black. Using ideas from quantum physics, he showed that they can give off a tiny bit of heat, now called Hawking radiation.
This means black holes lose energy slowly over time, and one day, they might even disappear completely.
๐ง The Big Puzzle: How to Mix Gravity and Quantum Physics
The problem is, Hawking had to mix two types of science to come up with his idea:
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General Relativity – the science of space, time, and gravity
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Quantum Mechanics – the science of tiny particles and energy
These two don’t always work well together. Scientists have been trying for decades to find a unified theory that explains both gravity and quantum physics in one neat formula.
And now, a group of scientists, led by Jalalzadeh, may have found a clue using an unusual tool: fractional calculus.
๐งฎ What Is Fractional Calculus?
You’ve probably heard of calculus, the type of math used to study change, speed, and curves. It uses operations called derivatives and integrals. Usually, we take whole-number derivatives, like 1st or 2nd derivatives.
But fractional calculus is a way to take half, quarter, or any non-integer derivative. Imagine taking the “half” of a change—not just a full one. This may sound weird, but it’s very useful for studying things that are messy, irregular, or spread out, like:
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Fluids flowing in weird ways
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Natural patterns like trees or rivers
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Brain signals
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Even quantum systems
Now, scientists are applying this math to the study of black holes—and it’s revealing amazing new results.
๐ The Wheeler–DeWitt Equation: A Tool for Quantum Gravity
To study black holes using quantum physics, scientists use something called the Wheeler–DeWitt (WDW) equation. Think of it like a big equation that tries to describe the entire universe—how it began, how it behaves, and even how black holes work.
Normally, this equation is solved using regular calculus. But in this new research, the scientists solved it using fractional calculus. This let them explore what happens when the shape of space and time itself becomes fuzzy or "fractal."
๐ What They Found: A Whole New Kind of Black Hole
Instead of the usual black hole with a smooth, round event horizon, the new math showed something strange. These black holes have:
๐น Fractal Horizons
Instead of a smooth outer layer, the surface is jagged and complicated—like a snowflake or mountain range. It's no longer 2D or 3D—it has a fractional dimension, something in between.
๐น Fixed Mass Levels
Just like electrons in an atom can only stay in certain orbits, these black holes can only have specific mass values. There is a lowest possible mass—called a ground state—that they can’t go below.
๐น Different Radiation
These black holes don’t shine smoothly like Hawking predicted. Instead, they emit radiation in specific frequencies, almost like musical notes.
๐น New Kind of Entropy
In simple terms, entropy is a measure of how much disorder or information a system has. In regular black holes, entropy depends on the surface area. But in these fractal black holes, entropy depends on a fractal surface area—a surface that changes based on scale.
๐น Colder Temperatures
Perhaps the biggest surprise: These black holes are much colder than regular ones. This means they give off very little energy and may last much longer, maybe even forever.
๐งฉ Why Are These Black Holes Fractal?
The key to this is a number called alpha (ฮฑ), which appears in fractional calculus. It can be any number between 0 and 2.
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If ฮฑ = 2, you get the usual black hole from regular physics.
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If ฮฑ < 2, you start to see fractal behavior—rough edges, weird shapes, and new rules.
This means space and time themselves may become fractal near a black hole. That’s a radical idea—our universe might not be smooth and continuous, but bumpy and strange at very tiny scales.
๐ How Does This Change Physics?
This new kind of black hole changes a lot of things we thought we knew:
๐ธ Black Hole Images
Scientists have already taken real pictures of black holes using the Event Horizon Telescope. In the future, we might see differences in shape or brightness that match what this new theory predicts.
๐ Gravitational Waves
When two black holes collide, they send out ripples called gravitational waves. If one or both are fractal black holes, these waves could carry new patterns or echoes that we can detect.
☀️ Solar System Tests
Even small differences in gravity could show up in how planets move or how light bends. This means we might be able to test some of these ideas right here in our solar system.
๐ What Comes Next: Spinning Black Holes
The current study only looked at non-spinning black holes (called Schwarzschild black holes). But in space, most black holes spin really fast. These are called Kerr black holes.
The scientists plan to use their method on spinning black holes next. This could reveal even stranger behaviors and possibly explain:
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Why black holes grow the way they do
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How they keep or lose information
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What really happens inside a black hole
๐ง Why This Is Exciting
This study shows that by using new math tools, we can discover new laws of nature. Fractional calculus is helping scientists go beyond the limits of Einstein’s theory and into the world of quantum gravity.
It’s also bringing us closer to answering the biggest questions in science:
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What is space made of?
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Is the universe smooth or rough at tiny scales?
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What happens inside a black hole?
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How do gravity and quantum physics fit together?
๐ Summary: Black Holes Are Getting Weirder—and That’s a Good Thing
Here’s what you should remember:
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Scientists used fractional calculus to solve a quantum gravity equation.
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They found new kinds of black holes with fractal shapes, fixed masses, and lower temperatures.
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These black holes don’t follow the usual rules and could help us discover new physics.
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Future research will study spinning black holes using the same method.
๐ฌ In Simple Words:
Black holes may not be smooth and round like we thought. They might be messy, jagged, and cold—just like some of the wild patterns we see in nature. And that may be the key to finally unlocking the secrets of our universe.
Reference: S. Jalalzadeh, H. Moradpour, G. R. Jafari, P. V. Moniz, "Fractional Schwarzschild-Tangherlini black hole with a fractal event horizon", Arxiv, 2025. https://arxiv.org/abs/2506.06031
Technical Terms
๐ณ Black Hole (BH)
A black hole is a region in space where gravity is so strong that nothing—not even light—can escape from it. It’s formed when a massive star collapses in on itself.
๐ง Hawking Radiation
A prediction by Stephen Hawking that black holes emit tiny amounts of energy due to quantum effects. This means black holes can slowly lose mass and may eventually disappear.
๐ Event Horizon
The "point of no return" around a black hole. Once something crosses this invisible boundary, it cannot come back out.
๐ Entropy
A measure of how much disorder, randomness, or information is in a system. For black holes, entropy is linked to the size of the event horizon.
๐งฎ Fractional Calculus
A branch of mathematics that allows us to do calculations using non-whole-number values, like half-derivatives or one-third integrals. It’s useful for studying complex or messy systems.
๐ Fractional Derivative
Instead of taking a full derivative (rate of change), a fractional derivative finds the change at a fractional rate, like 0.5 or 1.7. It lets us explore smoother or more spread-out behaviors.
๐ Wheeler–DeWitt (WDW) Equation
A very advanced equation used in quantum gravity. It tries to describe the entire universe—including black holes—by combining quantum physics and general relativity.
๐งฌ Quantum Gravity
A field of science trying to combine quantum mechanics (rules for tiny particles) and general relativity (rules for big things like planets and black holes) into one theory.
๐งฑ Fractal
A fractal is a shape or pattern that repeats at different scales and often looks rough or jagged. It’s not completely smooth, like a line or a circle, and may have a non-integer dimension.
๐งช Fractal Dimension
Instead of a normal shape having 1D (line), 2D (square), or 3D (cube), a fractal shape can have a dimension like 1.5 or 1.9. It’s somewhere in-between, showing that the shape is more complex.
๐ Mass Spectrum
The set of possible mass values that an object (like a black hole) can have. In quantum theory, objects often have only specific allowed mass levels.
๐ก Temperature (of a black hole)
This is related to how much Hawking radiation the black hole gives off. A colder black hole emits less radiation.
๐ต Frequency (of radiation)
Just like musical notes have different pitches, black holes emit radiation at certain frequencies—these are the "notes" of their radiation.
⚖ Gravitational Constant
A number that tells us how strong gravity is. In this theory, the gravitational constant can change depending on the scale and fractal dimension of space.
๐ญ Schwarzschild Black Hole
A simple, non-rotating black hole with no electric charge. It’s the basic model of a black hole from Einstein’s theory.
๐ Kerr Black Hole
A spinning black hole. Most real black holes in the universe are Kerr black holes because stars naturally spin before collapsing.
๐งฒ Non-local Effects
This means something happening in one place can affect something else far away—not just next to it. Fractional calculus includes these kinds of effects, which are important in quantum physics.
๐ Schwarzschild–Tangherlini Black Hole
A version of a black hole described in higher-dimensional spacetime. It’s an extension of the usual black hole idea to more than 3 dimensions.
๐ฏ Newtonian Gravitational Potential
This is a simpler, classical formula that describes how gravity pulls on objects. In the fractional black hole theory, even this simple gravity formula gets changed.
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