Theory · Advanced · 2:03

Hawking evaporation

A black hole's slow glow and last flash: how it would end, and what it would look like

Theory, not observation. Nothing here has ever been seen. Each idea comes from real physics and says how it could be made, and what it would look like. Light is bent as the equations say it would be; the things themselves are drawn.

Below are the 9 chapters of this simulation in Cosmic Scale: each one's caption, then the fuller explanation the app shows under “Read more”. Colours, arrows and lines mentioned in the text belong to the 3D scene in the app.

Open Cosmic Scale then the What if tab

1. A black hole that glows

A black hole is not quite black. In 1974 Stephen Hawking showed that quantum physics makes it glow faintly, and the heavier the hole, the colder the glow. A hole of one Sun's mass would be at 6.2 × 10⁻⁸ kelvin, far colder than anything in the sky.

Before this, a black hole was the perfect absorber: light goes in and nothing comes out, so it seemed to have no temperature at all. Jacob Bekenstein argued in 1972 that it should have one. Hawking first doubted him, then found in his own calculation that the hole really does radiate.

The temperature is ħc³ / 8πGMk, so it falls as the mass rises. For one Sun that is about 62 nanokelvin, and the glow carries only 9 × 10⁻²⁹ watts, while the sky's background radiation pours into the hole at hundreds of watts.

No one has seen this glow from a real black hole. Here it is drawn in pale blue, since it is far too faint to see. The black shadow and the stars bent round it are followed through the hole's geometry, as general relativity says.

2. Where the glow comes from

Empty space is never quite empty: pairs of particles flicker into being. Near the edge of a hole, Hawking found, one of a pair can escape and become real. The glow's wavelength is always about 16 times the hole's radius.

The picture of pairs is a rough one, and Hawking used it only to explain. His calculation treated quantum fields in the curved space of a star that collapses, and found that a long time after the collapse a far-away observer sees particles streaming out, in the pattern of a warm body's glow.

The size follows a neat rule: the glow's brightest wavelength is about 16 times the hole's radius, whatever its mass. A hole a few kilometres wide glows in radio waves tens of kilometres long. A hole the size of a proton would glow in gamma rays.

The energy comes out of the hole's own mass: each quantum that escapes takes a little with it, so the hole grows lighter. The sparks streaming out here are drawn, since no eye could see them.

3. How a hole is made

Every black hole is made the same way: squeeze matter into less than its radius of no return, 1.5 × 10⁻²⁷ metres for each kilogram. For the Earth that radius is 8.9 × 10⁻³ m, for the Sun 3.0 km. Nature does it when a heavy star's core collapses.

The recipe never changes: take a mass and get all of it inside a sphere of radius 2GM/c². The Earth would have to be squeezed to the size of a marble, the Sun to six kilometres across. Nothing is added: from far away the hole pulls just as the original did. Only very close does nothing get out.

Stars do it on their own. When a star of roughly twenty Suns or more runs out of fuel, its core can no longer hold itself up and collapses in a fraction of a second, leaving a hole of a few to tens of Suns. The picture follows it as a far-away watcher sees it: the surface creeps towards the horizon and its light fades in a few hundred millionths of a second (Oppenheimer and Snyder, 1939).

A tiny hole, one that would glow hot and die in our lifetime, is another matter. The smallest that theory allows has the Planck mass, 2.2 × 10⁻⁸ kilograms, and making it takes about 10¹⁶ TeV of energy. The Large Hadron Collider collides protons at 13.6 TeV, about a million billion times too little.

Some theories with extra hidden dimensions would lower that price to within the collider's reach, so its experiments searched for tiny holes that would evaporate at once. None has turned up. The tiny holes that nature might have made come later.

4. It shrinks, and it heats

Glowing costs mass. A lighter hole is hotter and gives out more, so the loss speeds up. A hole of one Sun would take 2.1 × 10⁶⁷ years to disappear, far longer than the 13.8 billion years the universe has lasted.

The rules are simple. Temperature goes as 1 over the mass, power as 1 over the mass squared, and the lifetime as the mass cubed: a hole twice as heavy lives eight times longer. Adding up the mass lost, moment by moment, gives Hawking's formula for the lifetime.

The chart follows one hole through its life. For nearly all of it almost nothing changes: halfway through, four fifths of the mass is still there. Only in the last moments does the mass drop away and the temperature soar.

This is Hawking's formula, which no one has tested on a real black hole. The glow in the picture is drawn.

5. The long wait

A hole colder than its surroundings takes in more than it gives out. The sky is filled with the Big Bang's afterglow at 2.7 kelvin; a hole of one Sun, at 6.2 × 10⁻⁸ kelvin, is growing. It can only start to shrink when the afterglow has cooled below that, in about 3.1 × 10¹¹ years.

The cosmic microwave background is 2.725 kelvin today and cools as space stretches. Only a hole lighter than about 4.5 × 10²² kilograms, six tenths of the Moon's mass, is hotter than the sky. Every hole made by a star is far heavier, so each still grows.

In the standard picture, dark energy keeps the stretching going for ever, and the background cools by a factor of e every 17 billion years. It takes about 18 of those to fall to a Sun-mass hole's temperature, some three hundred billion years from now.

The sky in the picture fades to show the wait. Long before then the stars will have burned out and the other galaxies will have faded from view. The fading is drawn.

6. The small ones

Stars only make black holes heavier than a few Suns. But in 1971 Hawking suggested that the crush of the early universe could have made tiny ones. One of 1.7 × 10¹¹ kilograms, the mass of a large hill, would be ending its life now.

Such a hole has a radius of about 2.6 × 10⁻¹⁶ metres, a third of a proton's, and glows at 7 × 10¹¹ kelvin. Its lifetime is the age of the universe: made at the very start, it would be dying today. Lighter ones would already be gone.

The idea is that regions of the early universe a little denser than average could have collapsed, as Zel'dovich and Novikov proposed in 1966 and Carr and Hawking worked out in 1974. Nothing shows that any did.

Heavier primordial holes would still be around, and some have been suggested as dark matter. Observations rule out most masses, but a few gaps remain open. The corner shows how small a dying hole would be beside a proton.

7. The last second

As the mass falls the glow brightens and the loss quickens. A second before the end the hole would have 2.3 × 10⁵ kilograms, and it would give out about 2.1 × 10²² joules: the energy of some five million megatons of TNT.

Then its temperature is about 5 × 10¹⁷ kelvin, far hotter than the collisions in the Large Hadron Collider. Every kind of particle there is would pour out, and maybe kinds not yet discovered, from a hole only 7 × 10⁻²² metres across.

What happens at the very end is not known. When the mass nears the Planck mass, about 22 micrograms, Hawking's calculation stops being reliable and a theory of quantum gravity is needed. The countdown gets there in about 10⁻³⁹ of a second. Some think a tiny remnant is left.

The picture shows the countdown: the hole shrinks, and the drawn glow spreads and brightens until the flash fills the view. It would be made of gamma rays and particles, which cannot be seen.

8. Where does the information go?

The glow seems to come out with no trace of what fell in: a book and a rock could make identical glows. But quantum physics says information is never destroyed. This information paradox is still one of the deepest puzzles in physics.

Hawking pointed to the trouble in 1976. A hole that evaporates completely leaves only thermal radiation, and thermal radiation is the same whatever made the hole. If so, what fell in is lost, which quantum mechanics forbids.

In 1993 Don Page showed how the radiation's entropy should behave if information survives: rising until about half the hole is gone, then falling back. Hawking's original calculation gives a curve that only rises. The corner sketches both.

In 2019 several groups got the falling part from calculations that count extra pieces of space called islands. These work in simplified models. For a real black hole the question is still open.

9. Has anyone seen one?

No. No black hole has ever been seen to glow, and no last flash of a tiny one has been found. But in 2016 Jeff Steinhauer saw a similar glow at the edge of a sonic "black hole" in a cloud of ultracold atoms.

Steinhauer's cloud of rubidium atoms flowed faster than sound in it, so sound waves could not come back out, as light cannot from a black hole. Pairs of sound quanta appeared at the edge in the pattern Hawking's method gives. It shows that the mathematics works; it is not gravity.

In the sky, searches for the final flashes of tiny holes have found none. Telescopes such as Fermi's Large Area Telescope and HAWC have limited such flashes to fewer than about ten thousand per cubic parsec per year.

So Hawking radiation is the best-loved prediction that no one has seen from a real black hole. Nothing here has been seen, and the glow and the flash in the pictures are drawn.

Objects in this story