A new study published in the Journal of Cosmology and Astroparticle Physics by three researchers at Radboud University in the Netherlands has dramatically revised our estimate of when the last objects in the universe will cease to exist.

That is a 1 followed by 78 zeros.

It sounds incomprehensibly long, and it is.

But it is also vastly shorter than the previous estimate of 10¹¹⁰⁰ years, which is a 1 followed by 1,100 zeros.

To put that difference in perspective: the gap between those two numbers is so enormous that no analogy from everyday life can adequately capture it.

The previous estimate was not just slightly wrong.

It was wrong by a margin that makes the difference between a second and the current age of the universe look trivial by comparison.

And the reason for the revision is a process called Hawking-like radiation, which turns out to apply not just to black holes, as was previously assumed, but to almost everything in existence. What Is Hawking Radiation, and Why Does It Matter?

In 1975, physicist Stephen Hawking proposed something that contradicted what many physicists believed about black holes.

He argued that black holes are not completely black. They leak. Very, very slowly. Hawking radiation 33a5ec1 An illustration showing what generates Hawking radiation. Credit: Getty Images

The popular explanation, the one Hawking himself used in talks and books, involves pairs of virtual particles that pop into existence near the edge of a black hole.

At the edge of a black hole, two temporary particles can form, and before they merge, one particle is sucked into the black hole and the other particle escapes, producing what is called Hawking radiation.

The particle that escapes carries energy with it.

That energy has to come from somewhere, and the somewhere is the black hole itself.

Over extraordinarily long timescales, the black hole loses mass and eventually evaporates entirely.

This contradicts Albert Einstein’s theory of relativity, which says that black holes can only grow.

It is worth noting that physicists now understand the virtual particle explanation to be a useful simplification rather than a fully accurate picture of what is happening.

The true mechanism is more subtle, involving the way that curved spacetime and quantum uncertainty interact to produce radiation from any region where gravity bends space strongly enough.

But the outcome is the same: black holes slowly radiate away their mass, and given enough time, they disappear. The 2023 Discovery That Changed Everything

The new study builds directly on a 2023 paper by the same trio: black hole expert Heino Falcke, quantum physicist Michael Wondrak, and mathematician Walter van Suijlekom.

In that earlier paper, they made a significant and surprising claim.

Hawking radiation is not unique to black holes.

Any object with a gravitational field can, in principle, evaporate via the same process.

They showed that not only black holes, but also other objects such as neutron stars, can evaporate via a process akin to Hawking radiation.

That finding raised an immediate follow-up question from the scientific community and from curious members of the public alike: if everything evaporates, how long does the process actually take?

After that publication, the researchers received many questions from inside and outside the scientific community about how long the process would take. They have now answered this question in the new article. How the Study Was Conducted

The team used mathematical calculations drawn from three different fields: astrophysics, quantum physics, and pure mathematics.

They worked through ten different types of objects, calculating from first principles how long each would take to evaporate via Hawking-like radiation in an ideal environment with no other influences.

The calculations further showed that the evaporation time of an object depends only on its density.

That is a deceptively elegant result.

It means that the clock for how long an object lasts has nothing to do with its size, its composition, or its history.

Only its density determines its fate. Findings From the Study

The results produced a table of cosmic lifetimes that is simultaneously mind-bending and strangely clarifying.

The most significant finding concerns white dwarf stars, which the researchers identify as the last survivors in the universe.

White dwarf stars dissolve in about 10⁷⁸ years. Previous studies, which did not take this effect into account, put the lifetime of white dwarfs at 10¹¹⁰⁰ years.

White dwarfs are the dense, cooling remnants left behind when stars like our Sun have exhausted their nuclear fuel. opo9532c A Hubble Space Telescope colour image of a small portion of the cluster only 0.63 light-years across reveals eight white dwarf stars among the cluster’s much brighter population. White dwarf stars, the dense cooling remnants of stars like our Sun, are predicted to be the last stellar objects to evaporate via Hawking-like radiation, dissolving after about 10⁷⁸ years. About 97% of Milky Way stars will end up as white dwarfs.

They are not actively burning anything.

They are simply cooling down, extremely slowly, over immense stretches of time.

Approximately 97 percent of the stars in the Milky Way will eventually become white dwarfs.

They are, in essence, the embers of the universe.

And according to this new research, those embers will finally go cold and vanish at around 10⁷⁸ years. The Counterintuitive Finding About Black Holes

One of the most striking results in the paper concerns the relative lifetimes of neutron stars and black holes.

Common sense would suggest that black holes, with their extraordinarily powerful gravitational fields, should evaporate faster via Hawking radiation.

A stronger gravitational field should produce more radiation.

More radiation should mean faster decay.

But the calculations produced a surprising result. Black Hole b707c6a

To the researchers’ surprise, neutron stars and stellar black holes take the same amount of time to decay: 10⁶⁷ years. This was unexpected because black holes have a stronger gravitational field, which should cause them to evaporate faster.

The reason turns out to come down to geometry.

Black holes have no surface. They reabsorb some of their own radiation, which inhibits the process, said co-author and postdoctoral researcher Michael Wondrak.

A neutron star has a surface.

Radiation that leaves a neutron star is gone, contributing to the evaporation process without being recaptured.

A black hole, by contrast, has an event horizon, and some of the radiation it produces loops back inward and is reabsorbed.

The two effects cancel each other out, and the two objects end up with essentially the same lifespan.

This is not a trivial result.

It tells us something fundamental about the relationship between the geometry of objects and the rate at which they decay. What Makes This Genuinely Surprising

Most people, when they think about the death of the universe, picture it as something that happens to the grand structures: the galaxies, the clusters, the supermassive black holes at the heart of everything.

The intuition is that ordinary matter, the atoms, the rocks, the planets, will long outlast the exotic celestial objects.

The new research overturns that intuition in an interesting way.

Because the researchers were at it anyway, they also calculated how long it takes for the Moon and a human to evaporate via Hawking-like radiation. That is 10⁹⁰ years.

That is longer than the 10⁷⁸ years it takes a white dwarf to dissolve.

So in the Hawking radiation picture, the Moon and a hypothetical human body would outlast the last stars in the universe.

Of course, the researchers note with characteristic understatement that there are other processes that may cause humans and the moon to disappear faster than calculated.

Practically speaking, neither the Moon nor any human will be around in anything close to 10⁷⁸ years.

The Sun will swell into a red giant in about five billion years, consuming the inner solar system.

But taken purely as a calculation of Hawking-like evaporation in ideal conditions, the math tells us that less dense objects take longer to decay.

Since the Moon and a human body are far less dense than a white dwarf, they would take longer to evaporate via this mechanism.

It is a result that is genuinely funny if you think about it too long How This Applies to Our Understanding of the Universe

The study is clear that it addresses only Hawking-like radiation in isolation.

The actual end of the universe involves many other processes, some of which are better understood and some of which remain deeply mysterious.

The long-term fate of the cosmos depends on the nature of dark energy, the behaviour of protons over cosmological timescales, and phenomena that current physics cannot fully predict.

But what this research does is establish something important: the upper limit on how long stellar remnants can last.

Even if every other physical process were somehow paused, Hawking-like radiation alone would guarantee the universe cannot persist beyond approximately 10⁷⁸ years.

That is why the paper is titled precisely as it is: an upper limit to the lifetime of stellar remnants.

Professor Walter van Suijlekom, professor of mathematics at Radboud University, adds that the research is an exciting collaboration of different disciplines and that combining astrophysics, quantum physics and mathematics leads to new insights. “By asking these kinds of questions and looking at extreme cases, we want to better understand the theory, and perhaps one day, we will unravel the mystery of Hawking radiation.”

That last point is the deeper motivation behind the work.

Hawking radiation has never been directly observed.

It is almost certainly undetectable with any instrument that currently exists or that could be built in the foreseeable future, because for stellar-mass black holes the radiation is far too faint to measure against the cosmic background.

Calculating its effects across the full range of objects in the universe, and identifying unexpected results like the equivalence of black hole and neutron star lifetimes, is one of the few ways physicists can probe and test the theory indirectly. Holding the Numbers in Mind

There is a particular kind of vertigo that comes from trying to comprehend numbers like 10⁷⁸.

The universe is currently about 13.8 billion years old, which is roughly 10¹⁰ years.

The new estimate for the end of the universe is 10⁷⁸ years, which means the time remaining is longer than the current age of the universe by a factor of about 10⁶⁸.

That is a 1 followed by 68 zeros.

Every event that has ever occurred in the history of the cosmos, from the Big Bang to the formation of the first stars, from the emergence of life on Earth to this very moment, has taken place within the first 10⁻⁶⁸ of the universe’s total lifespan under the new estimate.

We are, cosmically speaking, in the very earliest fraction of a fraction of a second after the opening.

“So the ultimate end of the universe comes much sooner than expected, but fortunately it still takes a very long time,” said lead author Heino Falcke.

That statement is delivered with the calm of a scientist who has spent a long time sitting with these numbers.

It is also, in its quiet way, an unexpectedly reassuring thing to hear.

The universe will end.

But not for a very long time.

And somewhere in the mathematics of how it will happen, in the way that curved space leaks energy and density determines fate, there is a kind of deep order to the process that scientists like Falcke, Wondrak, and Van Suijlekom are working, patiently and across disciplines, to understand. More Findings from the Study

The paper itself establishes several additional findings that are worth unpacking carefully, because they reveal a picture of the universe’s fate that is considerably richer and stranger than the headline number alone conveys.

One of the most technically striking results in the study concerns the precise mathematical relationship governing how long objects last.

The researchers found that the evaporation timescale, which they denote as tau, scales with the average mass density of an object according to the relationship tau proportional to density to the power of negative three halves.

In plain terms, this means that denser objects evaporate faster, and less dense objects last longer, regardless of how large or massive they are. This is a genuinely counterintuitive result, because our everyday instinct is that heavier, denser things are more durable.

In the language of Hawking-like radiation, the opposite is true. A teaspoon of neutron star material, the densest ordinary matter in the universe at roughly 300 million tonnes per teaspoon, will vanish far sooner than a region of diffuse interstellar gas spread across light-years of space.

The paper provides a cascade of specific lifetimes that make this density dependence vivid and almost philosophically disorienting.

Neutron stars, the collapsed remnants of massive stars that have exploded as supernovae, have densities in the range of 3.3 times 10¹⁴ grams per cubic centimetre. Their evaporation timescale under the new calculation is approximately 10⁶⁸ years.

White dwarfs, which are less dense because they are the remnants of lighter stars like our Sun, evaporate in approximately 10⁷⁸ years.

The Moon, with a density of about 3.4 grams per cubic centimetre, a density comparable to granite, would take approximately 3 times 10⁸⁹ years to evaporate.

An object with the density of water would last approximately 10⁹⁰ years.

The Local Interstellar Cloud, the diffuse bubble of gas and plasma in which our solar system currently sits, with a density of roughly 5 times 10⁻²⁵ grams per cubic centimetre, would persist for approximately 10¹²⁷ years.

A supercluster dark matter halo, representing the largest and most diffuse gravitationally bound structures in the universe, would survive for approximately 10¹³⁵ years.

These numbers establish a clear and elegant ordering. The universe does not end all at once. It unravels in sequence, with its densest objects dissolving first and its most diffuse structures persisting almost unimaginably longer.

The white dwarfs that define the study’s headline result sit at a middle point in this sequence. They are the last dense stellar objects to disappear, but they vanish long before the most rarefied cosmic structures reach the end of their allotted time. The Explosive End of Neutron Stars

One of the more dramatic implications buried in the paper concerns what actually happens to neutron stars at the end of their evaporation.

The researchers note that neutron stars have a minimum stable mass, approximately 0.1 solar masses, below which they cannot maintain structural stability. As a neutron star slowly loses mass through Hawking-like radiation over the course of 10⁶⁸ years, it gradually approaches this critical threshold.

For a neutron star, the evaporation process can continue only until their minimum mass is reached, when it will explode and produce an observable burst of high-energy particles and neutrinos.

This is a remarkable detail.

The death of a neutron star under this process is not a quiet fade into darkness but an explosive event, a burst of high-energy particles and neutrinos marking the moment when the object finally crosses the boundary of instability.

The paper notes soberly that given the timescales involved, no neutron star formed in our current universe would ever reach this end point through Hawking-like radiation alone. The timescale is simply too vast.

But the possibility exists as a theoretical endpoint, and it connects the most exotic prediction of the study to the observable physics of energetic astrophysical transients.

White dwarfs, the paper notes, would meet a similar explosive fate as they approach instability at the end of their 10⁷⁸-year lifetime. What the Density Formula Reveals About the Very Early Universe

The density-based formula for evaporation time has an implication that points backwards in time rather than forwards.

The study calculates that primordial objects with densities above approximately 3 times 10⁵³ grams per cubic centimetre should have dissolved by now.

That threshold density, which the paper calls the maximum quasi-stable density for the present age of the universe, is an extraordinary number in its own right. It is roughly 10³⁹ times the density of a neutron star, and sits far below the Planck density, which represents the density at which quantum gravity effects are expected to dominate.

The implication is that if any extremely dense objects formed in the very early universe, perhaps in the exotic conditions of the first moments after the Big Bang, they would not have survived to the present day.

They would have decayed through gravitational pair production on timescales shorter than the current age of the universe.

This places the new research in dialogue with cosmological models of the early universe and with questions about what primordial objects might have existed in those first moments. If such high-density primordial relics had formed, the Radboud team’s calculations suggest they are already gone. The Question of Fossil Remnants From Previous Universes

The paper takes one further speculative step that is worth dwelling on, because it touches on questions that push right to the boundary between established physics and deep cosmological uncertainty.

Some theoretical frameworks propose that our universe may not be the first or only universe, and that some form of cyclical or recurrent universe formation might have occurred.

In such a scenario, stellar remnants from a previous universe, what the paper calls fossil stellar remnants, might in principle have survived into our current universe.

Fossil stellar remnants from a previous universe could be present in our current universe only if the recurrence time of star-forming universes is smaller than about 10⁶⁸ years.

This is the lifetime of a neutron star under the new calculations.

The logic is as follows. If a neutron star forms in a previous universe and survives into ours, then the time between that previous universe and ours must be shorter than the time it takes a neutron star to evaporate. If the gap between universes exceeds 10⁶⁸ years, no neutron star could survive the crossing.

The paper notes that such fossil objects would not be quietly sitting in space doing nothing. By the time our universe reached its current age, they would be accreting material from the intergalactic medium and the cosmic microwave background, growing rather than shrinking.

The researchers suggest that surveys designed to detect isolated stellar remnants, for example through gravitational microlensing, might in principle be used to search for or rule out such fossil populations, which would place constraints on multiverse scenarios.

The paper acknowledges frankly that this remains speculative, and that the likelihood of actually detecting such objects is presumably small.

But the fact that a paper about Hawking radiation timescales can make contact with questions about the recurrence of universes is a reminder of how interconnected the deepest questions in physics tend to be. The Coupling Parameter and What It Changes

The study introduces a technical parameter called the gravitational coupling parameter, denoted xi, which describes how the quantum field responsible for the emitted radiation couples to the gravitational field of the object.

Two specific values of this parameter are particularly meaningful.

When xi equals zero, the field couples to gravity in a minimal way, and this represents something like graviton-like emission, particles that couple to the curvature of spacetime itself.

When xi equals one-sixth, the field is conformally coupled, meaning it responds to gravity in a way that is scale-invariant, and this is more representative of photon-like emission.

The paper finds that the total energy emitted depends on which coupling is assumed, with graviton-like coupling producing significantly more emission from the interior of a compact object than photon-like coupling does.

For a neutron star-like object, graviton-like coupling can produce interior emission that is an order of magnitude higher than the exterior emission alone. For photon-like coupling, the interior contribution is still present but contributes only a factor of roughly 1.5 above the exterior emission.

This matters for interpreting the results because the precise lifetime of a given object depends on which type of field is dominant in the evaporation process. The headline number of 10⁷⁸ years for white dwarfs is calculated for the graviton-like coupling case.

The paper explicitly states that the coupling parameter introduces a scaling factor of at most 2.5 in the total energy flux, meaning that the lifetime estimates are correct to within roughly an order of magnitude regardless of which coupling value is most physically appropriate.

For a popular science discussion, the key takeaway is that the headline numbers are robust estimates rather than precise predictions, but they are not just rough guesses. The underlying mathematics constrains them within a factor of a few in any direction.

The Surface Emission That Black Holes Cannot Produce

One of the genuinely new theoretical contributions of this paper, as opposed to simply applying an existing framework to new objects, concerns the distinction between how black holes and non-black-hole objects emit radiation.

For a black hole, the only radiation an observer at a great distance can measure is the component that escapes directly from the region around the event horizon. There is no surface. The radiation passes through nothing on its way out.

For a neutron star or white dwarf, there is an additional radiation component.

Particles produced in the exterior space that cannot escape are absorbed by the compact object, increasing and redistributing its internal energy, leading to a surface emission with a blackbody spectrum.

This surface emission is absent from black holes by definition, because black holes have no surface. The radiation either escapes or falls in, and there is no physical boundary to absorb and re-emit.

The paper finds that for neutron-star-like objects at typical compactness, the surface emission component can be comparable to or even larger than the direct emission component, particularly for the graviton-like coupling case.

This is not just a technical detail. It represents a qualitative difference in the physical mechanism by which black holes and stellar remnants lose energy, even though the overall timescales turn out to be comparable. The Connection to the Information Paradox

The paper closes with an observation that opens onto one of the deepest unresolved problems in theoretical physics: the black hole information paradox.

The information paradox arises from the tension between two foundational principles. Quantum mechanics requires that information cannot be destroyed.

General relativity suggests that anything falling into a black hole is permanently inaccessible. If black holes evaporate completely through Hawking radiation, the information they swallowed appears to be gone forever, which violates quantum mechanics.

For black holes, this paradox has been debated for fifty years without resolution.

For neutron stars and white dwarfs evaporating via the Radboud mechanism, the situation is if anything more complicated.

Given that the emission of virtual pairs is separated from the location of decaying matter within the limits of the Heisenberg uncertainty principle, and that it is not a priori clear which of the two particles escapes or is absorbed by the surface, it is not immediately obvious how quantum information can be preserved within the context of gravitational pair creation.

Further work is needed to address these fundamental questions.

This is the paper ending not with a settled answer but with a genuinely open question.

The mechanism by which neutron stars and white dwarfs decay does not obviously preserve information, because the connection between the decaying matter deep inside the object and the radiation emitted far from its surface is mediated by quantum fluctuations in the spacetime itself.

Tracing the information content of the original object through that process is not straightforward, and the authors are candid that they do not yet have a solution. Why This Research Is Worth Taking Seriously

It would be reasonable to ask how much weight to place on calculations about events so remote in time that they bear no conceivable practical relevance to anything that could ever be observed or tested.

The researchers themselves address this directly in the paper.

Like Hawking radiation, this effect is not experimentally verified and there is little hope that this can ever be achieved for macroscopic objects, apart from experiments in analog gravity.

Analog gravity experiments create laboratory systems, often using flowing fluids or ultracold atomic gases, that mimic certain mathematical properties of curved spacetime.

These experiments have provided indirect support for some aspects of Hawking radiation physics, but they cannot directly test the evaporation of astrophysical objects.

The value of the research lies not in its practical applications but in what it reveals about the internal consistency and reach of physical theory.

When the same mathematical framework that describes Hawking radiation for black holes is extended to neutron stars and white dwarfs, it produces finite, calculable lifetimes.

The fact that those lifetimes are internally consistent, scale with density in a clean mathematical relationship, and produce unexpected but interpretable results like the equivalence of neutron star and black hole lifetimes, is evidence that the underlying physics is meaningful rather than arbitrary. The Simple Question at the Heart of It

There is something admirable about the directness of the question this research set out to answer.

After the 2023 paper showing that Hawking-like radiation applies to all objects with a gravitational field, the most natural follow-up question was: how long does it take?

The answer required combining astrophysics, quantum field theory on curved spacetime, and pure mathematics into a single calculation framework. It produced a result that was simultaneously reassuring and staggering.

The universe will end.

Everything in it will eventually dissolve through the slow, patient action of quantum fluctuations in the fabric of space itself.

But the timescales involved are so vast that they make the current age of the universe look like the first moment of the first second of the first day of creation.

As the paper’s lead author said with characteristic understatement: the ultimate end of the universe comes much sooner than expected, but fortunately it still takes a very long time.

That combination of rigour and quiet wit, doing the calculations dead-seriously and with a wink as the Radboud University press release put it, captures something important about how physics at the frontier of human knowledge actually gets done.

The universe is decaying.

Every object in it is slowly dissolving into radiation through a process so faint that it produces roughly one proton’s worth of decay in the Moon every 10⁴⁰ years.

And three physicists in Nijmegen sat down, did the mathematics carefully and correctly, and told us when the last ember will finally go out.