Black holes are among the most fascinating and mysterious objects in the universe. Astronomers have discovered black holes of very different sizes:
Stellar-mass black holes, a few times heavier than the Sun
Intermediate-mass black holes (IMBHs), thousands to millions of times the Sun’s mass
Supermassive black holes (SMBHs), billions of times heavier than the Sun, sitting at the centers of galaxies
What makes this puzzling is that some supermassive black holes already existed when the universe was very young. According to standard theories, there simply was not enough time for them to grow so large. So how did they form so quickly?
A recent study by Kallifatides, Papanikolaou, and Saridakis proposes a powerful and surprisingly simple answer. Their work suggests that primordial black holes, formed shortly after the Big Bang, could grow extremely fast by absorbing radiation from their hot surroundings—without needing any exotic new physics.
What Are Primordial Black Holes?
Primordial black holes (PBHs) are hypothetical black holes that may have formed in the very early universe, long before stars and galaxies existed. Instead of forming from collapsing stars, PBHs could have formed from dense regions of matter and energy created shortly after the Big Bang.
Because the early universe was extremely hot and dense, PBHs could have formed with a wide range of masses—from tiny to very large. For decades, scientists have wondered whether these PBHs could be the “seeds” that later became today’s massive black holes.
The key question has always been: Can PBHs grow fast enough?
Radiation: A Powerful Fuel in the Early Universe
In the early universe, especially during the radiation-dominated era, everything was filled with intense radiation. Temperatures were enormously high, far hotter than anything we observe today.
Black holes have a temperature too, known as the Hawking temperature. Smaller black holes are hotter; larger ones are colder. If a black hole is surrounded by an environment that is hotter than the black hole itself, it can absorb more energy than it emits.
This is where the new idea comes in.
Using the Full Stefan–Boltzmann Law
The researchers studied how black holes exchange energy with their environment using the Stefan–Boltzmann law, a fundamental rule of physics that describes how objects emit and absorb radiation.
They applied this law carefully to black holes immersed in a hot cosmic plasma. Crucially, they introduced a principle called isonomy, which means:
All particle species contribute to radiation absorption in the same way they contribute to Hawking radiation emission.
This ensures consistency and avoids unfairly favoring one process over another.
The result is striking:
When the surrounding universe is hotter than the black hole, the black hole grows—sometimes extremely fast.
Critical Collapse and the Role of γ (Gamma)
PBHs are thought to form through a process called near-critical gravitational collapse. In this process, the initial mass of a black hole depends on a parameter called the critical exponent, denoted by γ (gamma).
The researchers found that when γ lies in the range:
0.33 < γ < 0.49
and especially when γ is very close to its critical value (around 0.495), something dramatic happens.
Even small black holes can grow explosively by absorbing radiation.
A Shocking Result: From Modest to Massive in 58 Days
The study shows that a primordial black hole formed during Big Bang Nucleosynthesis (BBN) with a mass of about:
10⁶ solar masses
can grow to:
~10¹⁰ solar masses
in just:
~10⁶ seconds (about 58 days)
Yes—less than two months.
On cosmic time scales, this is essentially instantaneous.
This means that some supermassive black holes may have acquired most of their mass within the first month of the universe’s history.
A Natural Explanation for All Black Hole Sizes
One of the most powerful outcomes of this work is that it produces a continuous black hole mass spectrum.
Small variations in the value of γ—affected by the number of relativistic particles in the early universe—lead to huge differences in final black hole mass. This naturally creates:
Stellar-mass black holes
Intermediate-mass black holes
Supermassive black holes
—all from the same physical process.
There are no artificial gaps between mass ranges, which matches astronomical observations very well.
Conservative and Robust Assumptions
Importantly, the authors take a conservative approach. They assume that radiation is absorbed only over the black hole’s horizon area, even though physics suggests the effective capture area could be larger.
This means their estimates are likely understated rather than exaggerated.
Their conclusions do not depend on fine details or special assumptions—only on basic thermodynamics and known physics.
What Was Not Included (Yet)
To keep the analysis clean, the study does not include:
Black hole spin
Black hole mergers
Detailed effects on gravitational-wave backgrounds
These factors will be important in future studies, especially for comparing predictions with observations from telescopes and pulsar timing arrays.
A New Picture of Cosmic History
If this mechanism is correct, it completely reshapes our understanding of black hole formation.
Instead of slowly growing over billions of years, many black holes may have:
Formed very early
Grown extremely fast
Reached near-final mass within weeks
This explains why supermassive black holes appear so early in cosmic history—and does so using only standard physics.
Final Thoughts
The work of Kallifatides, Papanikolaou, and Saridakis highlights a previously overlooked growth channel for primordial black holes: rapid radiative absorption in the early universe.
Their results suggest that:
Tiny primordial black holes could become cosmic giants
All known black hole mass ranges share a common origin
Supermassive black holes may have formed astonishingly early
This elegant and physically grounded idea opens exciting new paths for understanding the universe—and invites future tests using observations of quasars, gravitational waves, and the early cosmos.
Reference: Dimitris S. Kallifatides, Theodoros Papanikolaou, Emmanuel N. Saridakis, "Ultra-fast growth of primordial black holes through radiative absorption", Arxiv, 2025. https://arxiv.org/abs/2601.18708
Technical Terms
Primordial Black Holes (PBHs)
Primordial black holes are black holes that may have formed very early in the universe, just after the Big Bang. Unlike normal black holes, they did not form from dying stars but from extremely dense regions of matter and energy in the young universe.
Radiation-Dominated Era
This is an early period of the universe when radiation (light and energetic particles) was more important than matter. During this time, the universe was extremely hot and filled with high-energy particles.
Hawking Radiation
Hawking radiation is a process by which black holes slowly lose energy and mass by emitting particles due to quantum effects near their surface. Smaller black holes emit more Hawking radiation than larger ones.
Black Hole Temperature (Hawking Temperature)
Black holes have a temperature linked to their mass.
Small black holes are hot
Large black holes are cold
If the surrounding environment is hotter than the black hole, the black hole can absorb more energy than it emits.
Stefan–Boltzmann Law
This is a basic law of physics that describes how objects emit and absorb heat through radiation. It states that hotter objects exchange energy much faster than cooler ones.
Radiative Absorption
Radiative absorption means a black hole gaining energy and mass by absorbing radiation (heat and particles) from its surroundings.
Isonomy (Principle of Isonomy)
Isonomy means treating all particle types equally. In this context, it ensures that particles absorbed by a black hole follow the same physical rules as particles emitted by Hawking radiation.
Schwarzschild Black Hole
A Schwarzschild black hole is the simplest type of black hole. It does not rotate and has no electric charge. It is often used in studies because its behavior is easier to calculate.
Critical Collapse
Critical collapse is a process where matter is just dense enough to form a black hole. Small differences in initial conditions can lead to very different black hole masses.
Critical Exponent (γ or Gamma)
The critical exponent is a number that determines how massive a black hole becomes during critical collapse. Small changes in this number can cause large changes in black hole mass.
Big Bang Nucleosynthesis (BBN)
BBN is a short period, a few minutes after the Big Bang, when the first atomic nuclei (like hydrogen and helium) were formed.
Relativistic Species
Relativistic species are particles that move close to the speed of light because they have very high energy. Examples include photons and very energetic particles in the early universe.
Photon Sphere
The photon sphere is a region around a black hole where light can orbit due to strong gravity. It defines how effectively a black hole can capture incoming radiation.
Event Horizon
The event horizon is the boundary of a black hole. Once anything crosses this boundary, it cannot escape—not even light.
Backreaction
Backreaction refers to the effect that a growing black hole has on its surroundings, such as draining energy from nearby radiation and changing the environment.
Cosmic Time
Cosmic time is the measure of time since the Big Bang, used to describe events in the history of the universe.
Continuous Mass Spectrum
A continuous mass spectrum means black holes can have any mass within a range, rather than forming only at specific sizes.
Intermediate-Mass Black Holes (IMBHs)
IMBHs are black holes with masses between stellar-mass and supermassive black holes, typically thousands to millions of times the mass of the Sun.
Supermassive Black Holes (SMBHs)
SMBHs are extremely large black holes found at the centers of galaxies, with masses millions to billions of times that of the Sun.

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