Eternity is a very long time. The human brain can’t really wrap its head around the concept of infinity. Especially infinite time; no matter how many novels are written contemplating the idea of immortality. When thinking about how black holes form and grow, it’s inevitable that we wonder whether they too can die. Are black holes eternal and immortal, living for ever as the Universe evolves, with matter forever trapped inside the prison of the event horizon? Or is there a way they can eventually die?

It was British physicist Stephen Hawking who contemplated this question in 1974. Hawking’s life is truly extraordinary. In 1963, at the age of twenty-one, just six months after starting his PhD in cosmology at Cambridge University, Hawking was diagnosed with early onset motor neurone disease; an affliction that limits someone’s control of their voluntary muscles, which control speaking, eating and walking. His doctors advised him he had two years to live, and at that point he felt there was little reason to continue with his studies. With his disease progressing slower than first thought, and his mind unaffected, his PhD supervisor Dennis Sciama encouraged him to return to his research on singularities. In his PhD thesis, Hawking explored the idea that the Universe itself could have started in a singularity, an idea that would revolutionise cosmology through the application of general relativity.

With the discovery of neutron stars in the late 1960s and with Hawking’s work on singularities (applied to both black holes and the beginning of the Universe), the idea of a black hole was becoming more generally accepted, at least in the theoretical physics community, but there were many questions. Black holes, when you first consider them, seem to break many laws of physics, one of the most basic being the second law of thermodynamics: that entropy must always increase. Entropy is often described as a measure of disorder, but a better description might just be that whatever is the most likely thing to happen, will happen. If you fill a box with coins all heads up and shake it up, it’s very unlikely all the coins will stay heads up, or end up all tails. Instead, the most likely thing that will happen is that you’ll end up with a mess of roughly half heads up and half heads down. Crack an egg into a jar and then shake it up, the most likely thing that will happen is that the yolk will not remain whole. This is an especially good example, as the process of scrambling the egg is irreversible: you can’t unscramble the egg because entropy cannot decrease.

As matter is accreted by a black hole, it is locked away nice and neatly beyond the event horizon for evermore. This process removes a bit of disorder from the Universe, decreasing the entropy, seeming to violate that fundamental second law of thermodynamics. It was in 1972 that Mexican-born Israeli-American Jacob Bekenstein (then a PhD student at Princeton University) solved this issue.¹¹⁴ He realised that as the black hole accretes more matter, and grows in mass, its event horizon also grows. The event horizon is a sphere around the singularity, and so technically that sphere has a ‘surface’, with a surface area. As the black hole grows, the surface area of the event horizon sphere also grows. It’s this area that Bekenstein argued characterises the entropy of the black hole; as it grows the entropy increases and cancels out the lost entropy of the matter falling in. The overall entropy of the Universe still increases, as the second law of thermodynamics decrees.

Hawking, however, wasn’t so sure. Entropy is intrinsically linked to the amount of heat energy a process gives off, hence ‘thermo’-dynamics. A change in entropy is linked to heat transfer from hot to cold; for spontaneous transfer of heat energy from cold to hot, entropy would have to decrease – it is the least likely thing to occur. This is why a hot drink cools down and cold drinks warm up; heat is transferred from hot to cold as it’s the most likely thing to occur. Hawking reasoned that if the surface of the event horizon had entropy then it should be emitting radiation.

Hawking set about to disprove this and he knew to do it he would need to tie in quantum mechanics with general relativity. Quantum mechanics is what underpins the behaviour of particles on the smallest scales and it’s what gives rise to the laws of thermodynamics. Since general relativity can’t help us understand much beyond the idea of a singularity and an event horizon, could a quantum gravity theory help explain what was going on?

In 1973, Hawking visited Moscow to work with Soviet astrophysicists Yakov Zel’dovich and Alexei Starobinsky, who had been applying the ideas of quantum mechanics in the case of extremely curved space, such as around a black hole. They knew that curved space would wreak havoc with the balance of energy in space itself on tiny quantum scales. Much to Hawking’s disbelief, they had the mathematics to back up the claim that rotating black holes should be able to create and emit particles, which supported Bekenstein’s ideas about a black hole’s entropy.

To his annoyance and surprise, Hawking’s own initial calculations then showed the same thing (and that non-rotating black holes should also be able to create particles), and it became an obsession to explain what was going on. To explain this fully, you need a theory of quantum gravity; a marriage of quantum mechanics and general relativity to figure out what happens to quantum energy fluctuations in curved space. Unfortunately for Hawking that didn’t exist, and it still doesn’t in 2022. So instead, he took a shortcut. He considered the quantum energy before and after a black hole had formed when space was and wasn’t curved.

The quantum mechanics world is a weird one. There is energy in space itself, thanks to tiny vibrations, or oscillations to give them their proper physics term. There are certain modes that those vibrations can have; imagine space is a string on a violin and the quantum modes are different notes.¹¹⁵ Put a finger down on a fret and you’ll change the note the string makes (i.e. the energy it vibrates with). Quantum oscillations are a bit different to music notes on strings though, because you can have positive and negative wavelengths which cancel each other out, making a perfect balance of energy (something we call the ‘vacuum state’).

Hawking argued that forming a black hole in the path of these quantum oscillations could cause modes with wavelengths similar to the event horizon to get disrupted, at which point they would be lost to the black hole. However, other modes of different wavelengths would avoid disruption and continue on their merry quantum way. This would disrupt the balance of energies in the quantum modes in space itself, meaning that some would no longer have another mode to cancel them out. This imbalance in energy gets released as real radiation; light with a wavelength similar to the size of the event horizon of the black hole. So the event horizons of supermassive black holes should emit radiation with a longer wavelength, like radio waves, and smaller black holes should emit radiation with a shorter wavelength, like X-rays or gamma rays, with power that is almost explosive. In fact, Hawking titled his paper describing this process as ‘Black hole explosions?’, although this radiation would eventually come to be known as Hawking radiation.

What was truly remarkable was that when Hawking worked through all the quantum mechanics mathematics to arrive at this conclusion, he realised that the distribution of different wavelengths of radiation given off would be the exact same shape as given off by thermal radiation from something hot like a star. Here again is a link between thermodynamics and the physics of black holes. In everyday thermodynamics, ‘black body radiation’ is radiation emitted by anything that is heating its surroundings, anything from a star, to an oven, to a human body. Whereas a massive star gives off the majority of its radiation at ultraviolet and optical wavelengths, a human body gives off the majority of its radiation in the infrared, at longer wavelengths. This is because a human is, unsurprisingly, much cooler than a star. For thermal radiation there is a very specific shape to the distribution of wavelengths of radiation given off that is related solely to an object’s temperature, a phenomenon that was discovered in 1900 by German physicist Max Planck, one of the pioneers of quantum mechanics. It’s why hotter stars are blue and cooler stars are red.

Hawking realised that the radiation produced as black holes disrupted these quantum energy oscillations could be described in the same way, except instead of temperature determining the shape of the distribution, it was the surface area of the event horizon (and therefore the mass of the black hole). Just as Bekenstein had theorised, but had not been able to explain. The big impact of Hawking radiation, though, is that to turn a tiny quantum oscillation into real emitted radiation, some of the energy in that process is borrowed from the black hole itself. Remember, in Einstein’s most famous equation, E = mc², energy and mass are equivalent. So as the black hole loses energy to produce Hawking radiation it also loses mass; the black hole slowly ‘evaporates’.

Emphasis there on the slowly. Hawking worked out how long this process would actually take, finding that it once again all depended on the mass of the black hole. A black hole the same mass as the Sun could hypothetically eventually evaporate away all its energy as Hawking radiation in a time of 10⁶⁴ years (that’s a 1 with 64 zeros after it, or 10,000 trillion trillion trillion trillion trillion years). Bear in mind the Universe itself has only been around for 13.8 billion years and you’ll realise just how sloth-like Hawking radiation truly is. Although Hawking did calculate that any primordial black holes that formed in the early Universe with a mass less than 1 trillion kg (for context, the Earth is around 6 trillion trillion kg, so Planet 9 is still safe, don’t worry) would have had enough time to evaporate by now.

What’s exciting is that if such black holes exist then we might just be able to spot their last gasps of Hawking radiation before they fully evaporate. In the last 0.1 seconds of this evaporation process, a 1 trillion kg black hole would emit the equivalent energy of a 1 million megaton hydrogen bomb. Sounds large, but it’s piddly, astronomically speaking; supernovae go off with energies 1 billion trillion times larger than that and radiate for days afterwards.

So while the hope has always been that we’ll observe Hawking radiation from a black hole in action, nothing has been detected yet. Hawking radiation remains hypothetical, a great idea on paper but not quite backed up with real data yet. That could just be because we haven’t waited around long enough to spot any; the process is so slow that a single human lifetime may not be enough time for radiation that we’d have a hope of detecting to be emitted.

The supermassive black hole at the centre of the Milky Way would be the most likely candidate, but at 4 million times the mass of the Sun, the Hawking radiation will have a long wavelength and be emitted at a much slower rate. It would take 10⁸⁷ years for it to fully evaporate, and that’s if it’s finished growing and doesn’t accrete more material in the future. For TON 618, reaching its maximum mass it can achieve through accretion, the evaporation time is almost 10¹⁰⁰ years (a googol). Whether the Milky Way’s own black hole or TON 618 will ever evaporate depends on how long the Universe will be around for. Does the Universe even have that many years left?