Can Black Holes Evaporate?

Black Holes are astrophysical objects that are so massive, that have gravity so high, that their escape velocity (some seven miles per second on Earth) exceeds the ultimate cosmic speed limit – the speed of light (186,000 miles per second). Since nothing can travel faster than the speed of light, nothing (matter and/or energy) once inside a Black Hole can ever get out again – or so the seemingly ironclad logic went.

However, that’s all according to classical physics. A physicist by the name of Jacob Bekenstein came up with the idea of applying quantum physics to these objects (upon a suggestion by his mentor John Wheeler – who incidentally coined the phrase “Black Hole”), and once that was done, well lo and behold, these objects apparently exhibited entropy, and therefore had a temperature and therefore must radiate and therefore can vomit out stuff. His ideas were mulled over and over again and finally agreed to and expanded on by the celebrated astrophysicist/cosmologist Stephen Hawking. That stuff that a Black Hole can regurgitate now goes under the name of Hawking radiation, or to give credit where credit is due it is technically Bekenstein-Hawking radiation. However, it’s usually just called Hawking radiation so I’ll stick with that convention.

Of course if Black Holes have a temperature, then they must follow the same laws of thermodynamics as any other object with temperature. One key point in thermodynamics is that energy exchanges between objects are at least partly determined by one object’s temperature compared to another object’s temperature. The temperature of a hot cup of coffee will stay hot longer the higher the temperature of the environment that surrounds that hot cup of coffee. A Black Hole’s temperature must be compared to whatever temperature surrounds that object when considering the fate of the Black Hole. So how does a Black Hole get temperature?

In retrospect, how this happens is obvious (as are all great ideas when applying hindsight).

There is no such thing as the perfect vacuum. That could only be achieved at a temperature of absolute zero where and when everything is 100% frozen stiff. Alas, such a state violates one of the most fundamental principles of quantum physics – the Heisenberg Uncertainty Principle – where it is impossible to know both the momentum and position of anything with 100% precision. If something were at absolute zero, frozen stiff and standing still, you’d know both the momentum (which would be zero) and position (at a standstill) of that something with absolute precision.

Since there is always a minimum state of energy anywhere in the Universe (something above absolute zero), and since energy and mass are equivalent (Einstein’s famous formula/equation), then that energy state, the false not-quite-absolute-zero vacuum, the vacuum energy*, can generate mass – virtual particles. However, the particles come in matter-antimatter pairs, which usually immediately annihilate and return to their former pure energy state. BUT, and there is always, a BUT – there’s an exception to the rule – that normal state of affairs can be thwarted.

The vacuum energy, that which can generate particle-antiparticle pairs, exists everywhere where existence has any meaning. Part of that existence is an area called the event horizon**, which is a concept related to the concept we call Black Holes. These cosmic objects all have an event horizon which surrounds them.

The event horizon surrounding a Black Hole is that somewhat fuzzy region that separates the region (below the event horizon) from which gravity rules over the speed of light, and that region (above the event horizon) where gravity’s escape velocity can’t quite dominate that speed of light velocity. I say its “fuzzy” since it’s not razor sharp, albeit nearly so.

The vacuum energy is part and parcel of the space surrounding the event horizon, above, below and spot-on. Now, what if that vacuum energy generates a pair of virtual particles, one each popping into existence above the event horizon; one below the event horizon. Then, the particles will be unable to annihilate and recombine into pure energy. One will stay within the Black Hole. The other, being above the event horizon, can be dealt a ‘get out of jail’ card. And thus, slowly, ever so slowly, but ever so surely, these cosmic sinks loses mass, thus energy, and they evaporate.

Here’s the general picture. Black Holes can only radiate from the event horizon region which, in a very large cosmic sink is going to be very cold because it’s not radiating very much, so initially only things like the mass-less photon escapes. Assuming there’s no incoming to replace the loss, the cosmic sink shrinks, and as it gets smaller it warms up slightly (that’s what things that shrink tend to do) and can radiate particles with small mass – say neutrinos. When the cosmic sink is tiny, it’s very warm, in a relative sense, and it can go out with a ‘bang’, maybe emitting an electron or positron which is way more massive. When there’s no more Black Hole, the vacuum energy still produces at random virtual particle pairs, but there’s no more event horizon from which to separate those virtual particle pairs and thus its all back to normal – the two annihilate and return to their vacuum energy state. That’s where the popular accounts end. End of story. The ultimate fate of Black Holes will be to evaporate via Hawking radiation, even if it does take trillions of years.

Alas, the written texts forget to mention that radiation emission (and other forms of emitted stuff) is a two-way street, not a one-way street. Black Holes can acquire stuff, as well as radiate stuff. If deposits exceed withdrawals, then these cosmic sinks will always have a positive ‘stuff’ balance and thus won’t fully evaporate. Now this is perhaps why Hawking radiation hasn’t been observed. The tiny amount of Hawking radiation (outgoing) will be swamped by the greater, many orders of magnitude greater, amounts of incoming radiation and other stuff impacting the Black Hole.

Forget these universal sinks (and their massive gravity) for a moment and concentrate on Planet Earth. Even at night, you see lots of suns – stars. You see them because they are radiating photons – particles of electromagnetic energy of which visible light is a small part. In fact you only detect a tiny fraction of visual photons because your visual detection devices (eyes) aren’t that efficient. Optical telescopes pick up a lot more of them, but they’re still just as real. You are also being hit by photons in the infrared, the ultraviolet, in radio wavelengths, X-ray photons, gamma-ray photons, etc. Though Earth’s atmosphere shields us from some of these photons (ultraviolet photons are far greater in number at the top of our atmosphere than at the bottom), you still get impacted by multi-billions of them; Planet Earth many orders of magnitude more. Some of the photons get reflected back into space; these don’t add to Earth’s energy/mass balance. Overall, there are roughly one billion photons for each and every fundamental particle with mass, like electrons and neutrinos.

Now in addition Earth (and you too) gets hit with cosmic rays, neutrinos, and cosmic dust. Even if you luck out, Planet Earth gets impacted by meteors and other outer space debris, sometimes debris large enough to not only hit the surface but do considerable damage. Planet Earth’s mass increases by many tons a day, all due to Earth’s sweeping up of the interplanetary dust and small rocks that intersect Earth’s orbit. The trillions of neutrinos that hit us are so ghostly that nearly all pass right through you and the entire planet as well despite them having a tiny amount of mass, so as far as our planet is concerned, they are of little significance.

Now what about a Black Hole? Clearly these objects aren’t isolated from the rest of the cosmos and other objects therein. If you were just outside the event horizon you’d ‘see’ photons (of all wavelengths) because you’d see stars and galaxies, etc. just like you can locally. Neutrinos would still pass right through you on their way to their doom once passing through the event horizon. The Universe is full of interstellar and intergalactic atoms and molecules and dust and of course lots of larger stuff a Black Hole can snack on. Black Holes will sweep up stuff just like Earth does, only more so since it has more gravity with which to grab hold of stuff with, and also because once caught there’s no escape for the cosmic fish. Unlike Earth, everything that crosses that event horizon, that hits the cosmic sink, won’t be reflected back (like photons). Neutrinos that can pass through light-years worth of solid lead without even ‘breathing hard’ will be imprisoned when they try that trick in a Black Hole’s inner sanctum. And of course atoms, molecules, interstellar dust, the big chunks will also get imprisoned.

But we can imagine an idealized cosmos where all Black Holes have swallowed up all existing radiated particles (photons), all the atoms, molecules, the dust and all the bigger stuff – all those stars and planets; asteroids and comets; even all that mysterious ‘dark matter’. So you have a cosmos of just universal cosmic sinks and the vacuum energy (well maybe a few bits and pieces escaped, but so few to be of no consequence). Of course there is one further logical extension. cosmic sinks can swallow other cosmic sinks. Black Holes can merge to form bigger Black Holes. The final product is that the cosmos consists of one Black Hole – the Mother of all cosmic sinks – plus the vacuum energy! So you end up with one Black Hole left standing with nothing left to eat.

Okay, so the only scenario now possible is that this Mother of all Black Holes evaporates via Hawking radiation. It might take trillions upon trillions upon trillions of years, but evaporate it does. Since matter and energy can neither be created nor destroyed, once the Mother of Black Holes has finally gone ‘poof’, the Universe is right back where it started from – full of stuff from photons to fundamental particles which them undergo chemistry to form atoms and molecules and stars and planets and perhaps life – and new Black Holes!

Perhaps this is a new and improved version of a cyclic/oscillating universe! – But then again, maybe not. There’s a fly in that ointment (but I had you going for a while back there!). That “idealized cosmos” was only a ‘what if’ thought experiment.

Firstly, it’s actually very, very unlikely all the Black Holes in the Universe will ever merge together as long as the Universe keeps expanding. Since the galaxies are getting farther and farther away from each other due to that expansion, the collection of Black Holes contained within each galaxy keep getting further and further apart from other clusters of Black Holes contained within other galaxies. It’s like the passengers in one car get more and more remote from the passengers in another car when each car is going at different velocities and heading in different directions.

Now the collection of all Black Holes in any one galaxy could well coalesce into one super Black Hole galaxy. You have a galaxy that instead of containing billions and billions of stars and debris and particles now consists of just one Black Hole – the car only has one occupant. You have a pure Black Hole galaxy, or a galactic sized Black Hole.

One might end up with a Universe composed of just these pure Black Hole galaxies, all spreading farther and farther apart over time.

But secondly, there’s another fly in the ointment. All the space that separates these pure Black Hole galaxies from each other isn’t a perfect vacuum, quite apart from the vacuum energy. All the radiating stars and stuff may have been gobbled up within each galaxy, but all of interplanetary space, all of interstellar space, and all of intergalactic space, isn’t pure vacuum. There’s still the ‘it’s everywhere, it’s everywhere’ Cosmic Microwave Background Radiation (CMBR).

So what’s this CMBR? If you have a massive hot explosion (like the Big Bang event is alleged to have been), and all that heat energy expands and expands, then you’d expect the temperature of the area occupied by that energy to drop, the temperature ever decreasing as the volume that finite amount of energy occupies increases. As the energy expands it gets diluted and thus cools, but can never reach an absolute zero temperature for reasons already noted. And that’s just what we find on a universal scale. There’s a fine microwave energy “hiss” representing a temperature a few degrees above absolute zero that’s absolutely everywhere in the cosmos. That’s the diluted heat energy of the very hot Big Bang – well it has been a long time since the Big Bang event (13.7 billion years worth of time) and that energy is now spread throughout a lot of cosmic volume. That microwave “hiss”, called the CMBR, was predicted way before it was discovered. There’s no doubt that it exists.

Since the CMBR is just photons with very long wavelengths, Black Holes could suck up the CMBR photons as easily as light photons. Removal of CMRB photons, already representing a temperature just slightly about the theoretical minimum – absolute zero – would mean the Universe gets even colder, which it would anyway since the Universe is ever expanding and thus available electromagnetic energy (photons) is ever diluting. Combining the two effects and the Universe is a chilly place indeed and will get even colder.

However, it’s probably not possible for Black Holes collectively to swallow up all of the CMBR since there will come a point of diminishing returns. What happens when the temperature of Black Holes equals the temperature of the Universe at large – the CMBR? The answer is thermal equilibrium like when your hot cup of coffee cools off to room temperature. Input into Black Holes from the CMBR will equal output via Hawking radiation. For every photon emitted via Hawking radiation, a CMBR photon gets sucked in. What does that mean? It means a Black Hole can not evaporate.

What about very tiny (micro) Black Holes that are relatively ‘hot’? Might they go ‘poof’ before thermal equilibrium is achieved? Will the contents of the Black Hole evaporate into the surrounding cosmos before they can equate to the surrounding temperature? The analogy might be like a hot drop of water could evaporate into the cold atmosphere before the liquid water drop can attain the temperature of its surrounding environment.

Even so, I still imagine that in the current matter and radiation dominated Universe, incoming would still exceed outgoing.

Of course if you could take a Black Hole, isolate and shield it from the rest of the cosmos and all that it contains, so all you have is the Black Hole and its internal energy (including the all pervading vacuum energy therein). An isolated Black Hole would be in a setting equivalent to putting it into an absolute zero temperature environment. If that’s the case then outgoing would exceed incoming since there could be no incoming, and therefore that Black Hole would then radiate and slowly evaporate and eventually go ‘poof’. BUT, and there’s always a BUT, I can not envision any scenario where a Black Hole can exist in such a theoretical isolation. So, Professor Hawking is quite correct – in theory. In practice, in the here and now, input exceeds Hawking radiation output, and even in the unimaginably far distant future equilibrium will be established where input equals output.

*If it helps to conceive of the concept of the vacuum energy, here’s an analogy. Think of the invisible but energetic atmosphere as the vacuum energy. Part of that atmosphere consists of invisible water vapour. But, all of a sudden, and for reasons that must have been mysterious to the ancients, part of the atmosphere undergoes a phase change into something you can see; into something solid – like a particle. You get mist/fog (clouds), rain drops, snow, sleet, hail, etc. Then, equally mysterious, those solid bits eventually undergo another phase change (evaporation standing in for annihilation) back to invisible water vapour in the equally invisible atmosphere. And so you have the invisible vacuum energy that generates particle-antiparticle pairs which annihilate back into the vacuum energy.

**The surface area of the event horizon is the same for both incoming and outgoing so there is no need to take that (non) variable under consideration.