Useful Notes / Black Holes

There are monsters out in the cosmos...
Full image here.

"Consideration of black holes suggests, not only that God does play dice, but that He sometimes confuses us by throwing them where they can't be seen."

— Stephen Hawking, The Nature of Space and Time

A black hole is a point of space so massive that even objects going at the speed of light (for example: light itself) cannot escape its gravity (thus the name). This phenomenon has fascinated scientists and writers of fiction for many, many years.

Black holes are collapsed stars, but not many people know how the stars have collapsed in such a way to create black holes. We don't really understand what a singularity (the heart of a black hole) even is. When we try to do the math, key calculations utterly collapse and physics melts down as the spacetime has infinite curvature. In other words, its mass has collapsed to paradoxically zero because it's infinitely small and infinitely dense--thus its gravity is infinitely intense.

Stars convert hydrogen into helium in their cores via fusion, which produces enormous amounts of energy; this balances out the inward pull of gravity and keeps the star stable. However, as the star ages, the hydrogen in the core starts to run out, the fusion reactions slow down, and gravity begins to collapse the star. At this point, a star of sufficient mass can begin to fuse helium, starting a cycle of fusions that produces increasingly heavier elements^note usually hydrogen -> helium -> carbon -> neon -> oxygen -> silicon -> iron, with the mass of the star determining how far the process goes and turns the star into a red giant or supergiant. However, even that can't go on forever. Stars that are massive enough can eventually fuse silicon into iron, but producing elements heavier than iron by fusion costs energy instead of producing it, so once the star builds up enough iron, fusion stops and its core completely collapses in on itself, creating a nova or supernova that blasts away most of the star's outer layers and leaves behind the collapsed core.

What form that core takes depends on its mass. For lighter stars, such as the Sun, the core becomes a degenerate-matter white dwarf which slowly cools over trillions of years into a black dwarf.^note Not to be confused with "brown dwarfs", which are sub-stellar bodies, like large planets, that were never massive enough to sustain fusion to begin with. According to current estimates, no black dwarfs yet exist, as a star cooling to that level would take longer than the universe has existed. The Sun is expected to become a black dwarf in approximately 1 quadrillion years. If the core is more than 1.4 times the mass of the Sun, it will exceed the Chandrasekhar limit and gravity will combine electrons and protons to form neutrons, resulting in a neutron star. If the core mass exceeds the Tolman-Oppenheimer-Volkoff limit (about two to three solar masses, and definitely no more than five, but it's still unclear), even the neutrons can't resist further collapse;^note Neutron stars are prevented from collapsing further by a pressure called neutron degeneracy pressure. This is caused by the Pauli exclusion principle, and the degeneracy pressure is insufficient to prevent collapse over the Tolman-Oppenheimer-Volkoff. However, it is possible that there are other forms of degenerate matter, which may be capable of preventing further collapse until the object's mass reaches a new limit. it can be assumed that the core collapses past its Schwarzchild radius,^note the radius of any object which, if crushed beyond that point, the object will form a black hole and becomes a singularity (a single point, or a ring for a rotating black hole).

Black holes can form from masses smaller than stars if the mass is under enough pressure, producing a "micro black hole". For instance, a human being could theoretically form a black hole, but you'd have to squeeze them into an area ten billion times smaller than the radius of a proton, and the same could theoretically be done to the Earth if you squashed it down to the size of a pea. However, this would likely require exotic physical conditions such as the ones existing right after the Big Bang.

Black holes are strange things. Besides the singularity at the center,^note Assuming it exists, since it's believed it's an artifact caused by breakdown of relativity under those conditions, that would disappear with a—still not existent—theory of quantum gravity there is the event horizon, the point of no return. Once inside the event horizon, you literally cannot go back: spacetime is curved in such a way by the black hole's mass that any path you take leads to the same place: the singularity. In three-dimensional space the black hole is not a disc, just like the Sun is not a big yellow circle. The Sun is a sphere, an event horizon is a smaller sphere, and the singularity is an infinitely tiny ball so small and tightly packed that it has basically turned itself inside out — so when you are inside the event horizon, you are inside the ball. Rotating black holes also have an ergosphere, a region near the event horizon where space-time spins around the black hole at speeds so great that you'd need to move faster than light just to stay still, let alone move in a direction counter to the black hole's rotation.

In fact, space-time will become quite freaky around the event horizon: the closer you get to it, the slower time becomes (due to relativity, but you won't notice it). In fact, if an observer outside the event horizon could see you, they would see as you get closer and closer (and get redder, due to gravitation red shift, while everything you see would be bluer), you would go slower and slower until you hit the edge of the event horizon at which point you would appear to stop. You won't actually stop, that's just what they'll see. This is because space-time around the black hole's event horizon is so warped that light would take a progressively longer time to reach a distant observer as you approach the event horizon — ad infinitum. They'd never see you actually touch the horizon, and the light you emitted would slowly be red-shifted to the point of invisibility. This prediction, however, assumes a zero-mass incoming object and neglects quantum effects, so reality may be more tricky.

Of course, nobody knows what'll happen after that, but there still are some theoretical predictions: You'll actually never even notice crossing it. You won't even fall into the apparent black void below you at all — it is in fact not the event horizon itself. You would just continue accelerating as the view before you warps into a straight line, until you hit the singularity and are compacted into an infinitely small point. Or you could find your molecules randomly rearranged as a small, green space-cat with tentacles for legs.

However, you'd probably be long dead before that anyway, as black holes come with some dangers attached due to the infinite gravity they exert. First, you'll be spaghettified (this is the scientific term for it): the tidal forces of the black hole are so strong that, if you were going in feet first, your feet would feel a stronger attraction than your head and thus your body would stretch out (incidentally, this occurs in more applicable situations, such as returning space shuttles, as well — the difference is that the attraction difference is so minor that the astronauts do not stretch a measurable amount). The gravity exerted by black holes is so strong that it can even deform atoms. On the upside, the bigger a black hole is, the less drastic this effect becomes on its edge. In fact, for a supermassive black hole, an individual should survive at least past the event horizon.^note For less massive ones, you'll be dead before you even cross the event horizon. The second big danger is good old radiation, due to gravitational blueshifting. Any radiation hitting you from the outside would be blueshifted (given higher frequencies, and therefore energy, as opposed to redshifting, which decreases the frequency of electromagnetic radiation and therefore their energy) and thus a lot more dangerous, to the point that, according to some simulations, it would be the thing that would kill you before you could reach the singularity, assuming a black hole big enough to neglect tidal effects. The thing is known as inflationary instability and, according to scientists, its effects would go very far beyond just vaporizing your body.

Black holes normally can't be seen (thus their moniker), but there are ways they are detectable. If they're siphoning off matter from a nearby star, they can form accretion disks, which get incredibly hot due to friction and other forces and emit light and other radiation at intensities on the order of millions of times the brightness of the sun. There's gravitational lensing, in which black holes are detected by the image distortions of objects behind them (The Other Wiki has a nice animation◊ for that). And then there's Hawking radiation, named after Stephen Hawking, who proposed the concept. It's a theoretical way for black holes to lose mass via quantum mechanics, and is a whole other can of non-zero entropy worms. One of its more practically relevant attributes is that the energy of the radiation "emitted" by a black hole is inversely proportional to its mass — the smaller it is, the faster it goes! In other words, really small ones, like the ones that the Large Hadron Collider might produce, would just evaporate and be gone before you even notice them (although the immense release of energy from the Hawking radiation would be noticeable). A solar-mass black hole, on the other hand, would lose about a milligram of its mass-energy every 3.1 x 10³¹ (31 nonillion) years, which they'd more than make up for by consuming the cosmic microwave background. A scientific paper proposes to use a small artificial black hole's Hawking radiation as a means to convert mundane matter into energy and thrust to power a spaceship.

In short: black holes are really, really weird. It's speculated that there are supermassive black holes at the center of every galaxy and that they were there before the galaxies formed (rather than just have formed by a variety of small black holes merging into one — yes, they can do that, and the simulations of that are pretty spectacular, but predict that the actual event is downright cataclysmic for anything too close). Note also that a merger of supermassive black holes can and does happen; this is in fact the inevitable result of galaxies merging, and is likely the source of quasars. At some point roughly 4 billion years in the future, this will happen to the Milky Way and Andromeda galaxies.

If all that still is not weird enough for your taste, look up Einstein-Rosen bridges (think wormholes, but it's rather useless from a practical point of view due to its instability) or really big, (insanely fast) rotating, charged black holes.

To learn more cool facts about black holes, please read David Morgan-Mar's rant here. Or this science question on Reddit. Seriously, they're awesome.

Another useful note is that black holes are one of the predictions derived from Einstein's theory of general relativity — and even in its context certain theorists saw the predictions of black holes in relativity and expressed doubts at least about the classical model. One such theorist was, initially, Einstein himself, who rejected the premise of a black hole rather strongly. Black holes just didn't make sense, especially how they muck up the nice wonderful understanding of space and time we (think we) have.

This means that other theories of relativity and gravity may or (more probably) may not allow similar effects. Thus, all bets are off the moment a fictional 'verse is described as having Faster-Than-Light Travel other than the rather weird Alcubierre Drive. Other signs that the universe is not compatible with General Relativity Theory (GRT) are mentions of either "gravitons" or "anti-gravitation": in GRT gravity isn't a proper field, but the curvature of space. GRT is not, as it stands, compatible with quantum mechanics, so it will probably eventually be extended through a field theory, the tradeoff being that a field theory does not only allow, but support the existence of repulsion forces, which no one has ever seen.

Until February 2016, with the first detection of gravitational waves with the LIGO instrument and other similar detections in the following years^note As most of the detected signals exactly match the theoretical predictions of a black hole merger, there was no strict proof that such things exist. Granted, there are heavy low-radiating objects ("black hole candidates"), but whether some low-emission star inside an enormous gas and dust cloud is really a black hole or not... Yet there is one article, that states: Sagittarius A* (a source of radio waves, associated with a supermassive object in the center of the Milky Way) must have an event horizon because, given the amount of superhot infalling matter we've detected around it, its surface luminosity is too low to be explained without something that traps radiation.^note That's part of the reason its name includes an asterisk, actually: We think there's a black hole there, but weren't completely sure; photographs would help, but there's currently many stars in the way, explaining why it took longer to image it.

In April 2019, a black hole was actually observed for the first time. The Event Horizon Telescope, a network of 8 interlinked telescopes, was able to photograph a black hole in the center of the distant giant galaxy M87, 500 million trillion km away (see the image that illustrates this article). This is roughly equivalent, in terms of scale, to reading the date on a coin in New York... from Los Angeles. The black hole looks like... a black hole, illuminated by the glowing ring of superheated gas around its event horizon. The internet immediately anthropomorphized it. Three years later, in May 2022, the team operating the same telescope released a picture of Sagittarius A* (the aforementioned supermassive black hole thought to exist at the heart of the Milky Way).

There is one last part about black holes that is still very controversial, the Black Hole Information Paradox. That is, what happens to information when in a black hole. Hawking stated that it's irretrievably lost, which would violate the First Law of Thermodynamics. However, thanks to the bizarre nature of black holes, it's possible the law might be broken (thank you, infinity). Other theories include it being hidden in a "pocket universe" or it's released when the black hole eventually evaporates, regardless of its size.

In a scenario somewhat related to the information paradox, black hole cosmology is arguably just as controversial, yet particularly interesting when you think about it. In this model of the Universe's creation, the 'nothing' outside the universe just so happens to be the inside of a black hole. Since time and space are infinitely vast at a black hole's singularity, this means the universe has an infinite amount of space to grow. This theory gets weirder still when you consider that if we're inside a black hole, then what about the black holes inside our universe? The result comes out looking something like a matryoshka doll, only that it's impossible to tell where it begins and where, if ever, it will end. Our universe could be just one of many, nested inside an infinite number of black holes containing other universes.

This is where things start to get even weirder. According to String Theory, black holes are actually "Fuzzballs", a ball of strings, bundles of energy vibrating in complex ways in both the three physical dimensions of space and compact directions — extra dimensions, interwoven in the quantum foam. This ties into the holographic principle. You are destroyed if you fall into one, and yet you are not. To resolve the information paradox, you are lost to the universe but absorbed by the black hole, ending up as a two-dimensional projection of your former three-dimensional self, trapped forever on the "fuzzy event-horizon". To the 3-D observer you are now 2-D, but you yourself would never ever know.

Some superstring theory scientists and physics theorize this has already happened, and that our entire true-3D or 4D universe has long fallen into a gargantuan black hole, and we ourselves are either in said black hole, or thanks to quantum mechanics ensuring information can never be created or destroyed, a part of the phenomenon. We are all preserved within the universe's ultimate hard-drive.

How big is a black hole?

A black hole's size — that is, the radius of its event horizon — depends on its mass, spin, and charge. The simplest case of an uncharged, non-spinning ("Schwarzschild") black hole has a surprisingly straightforward formula:

R_{Schwarzschild} = 3 km * mass in Solar masses

For astrophysics, this is more than sufficient to get a ballpark estimate of the size of any black hole based on the mass it contains. Thus, a black hole with a mass equal to the sun has an event horizon 3 kilometers in radius (6 km in diameter).

A black hole with a mass equal to the Earth (0.000003 solar masses) would have an event horizon whose radius was 0.000009 km, or 9 millimeters, or the size of your average American 1¢ penny.

A black hole with 4 million solar masses, such as Sagittarius A*, the black hole known to be at the center of the Milky Way, would have an event horizon whose radius was 12 million km, about a fifth of the orbital radius of Mercury^note Seventeen times larger than the Sun, comparable in size to a giant star such as Arcturus.

Going even further, the largest known black hole in the nearby universe, the already mentioned one located in the heart of the galaxy M87, with an estimated mass of 6.4 billion solar masses, would have a radius of 19.2 billion km, larger than our Solar System.

Further still: The galaxy NGC 4889 contains a supermassive black hole with a mass of 21 billion solar masses, meaning a radius of 63 billion km, and is at present the largest confirmed black hole in the known universe.

Perhaps even further: The ultra-luminous quasar TON-618, around 10.4 billion light-years distant, is calculated to possibly contain a central black hole massing in at 66 billion solar masses.^note For comparison purposes, this monster black hole is more massive than all the stars of the Milky Way galaxy combined. Scientists are calling it an "ultramassive black hole", because "supermassive" isn't a strong enough word to describe this behemoth. Its radius would be 1,300 AU, or 195 billion km.^note If you still do not have enough, some calculations show that in the very distant future, assuming an Universe in eternal expansion, the collapse of superclusters of galaxies could produce black holes with masses of up to one hundred trillion solar masses. Such monsters would have a radius of around 31 light years, or 295 trillion kilometers.

The odd thing about this, when compared with most "normal" spherically-shaped objects in the universe, is that the Square-Cube Law doesn't apply to them. Rather, a black hole's diameter is directly proportional to its mass — double the Schwarzschild radius and you've multiplied the mass by 2. For the average spherical object you and I might be familiar with, such as a ball of metal or water, the volume is proportional to its mass cubed — double the radius and you've multiplied the mass by 8. This means that the larger and more massive the black hole, the lower its average density.^note When discussing the density of the entire region inside the event horizon, not the density of the singularity at the center. A black hole with 1 solar mass would have an average density on the order of 10¹⁶ grams per cubic centimeter, about 1.5 quadrillion times the density of solid lead. A black hole with 4 million solar masses, on the other hand, would only have an average density of 0.00028 grams per cubic centimeter, about a quarter the density of air at sea level on the Earth, and the supermassive black hole mentioned above would be even less dense.

What isn't a black hole?

Black holes are not:

• Holes: They don't go anywhere. As far as the rest of the universe is concerned, you're right there. ^note In fact, one of the biggest problems with the definition of a black hole, mathematically, is that it seems to completely disregard the laws of thermodynamics (mass and energy are conserved via an increase in the black hole's mass and Hawking radiation). Stephen Hawking admitted that his math had a seriously big hole in the logic as a result, even though the rest added up. Theorists have posited several possible solutions to the problem. They don't look like they do in Science Fiction, you can't see them from that three-quarters angle that's popular, either. Assuming there's enough stars behind it, it'd just look like a big black spot maybe with a little light visible around the outside, depending on what's on the opposite side of you, but most of it would probably be red-shifted out of the visual spectrum. Instruments would be able to see much more exciting views in the form of various other kinds of radiation.
• Black: More specifically, while the hole itself is certainly black, as no light can escape from inside the event horizon, matter which happens to be falling into the black hole will form an accretion disk, and the matter in the disk glows very brightly due to the immense heat and other radiation generated by friction and other forces, and thus such a black hole can be one of the brightest objects in the universe. A real black hole might look more like this.◊
• Flat: Staying away from the more wibbly-wobbly stuff, it's convenient to think of a black hole as a tiny sphere and the event horizon as a shell around it. Once you hit the shell, you're stuck. It's also going to look pretty much exactly the same as you circle it, regardless of the direction you chose.^note Black holes that rotated very fast are expected to look distorted. The objects orbiting it do so due to spin.
• Whirlpools: Black holes don't gain any powers of suction when they become black holes. Their mass exerts the same gravitational force as a star, planet, or any other object of the same mass. If our Sun were suddenly turned into a black hole of the same mass, the Solar system would not get "sucked in." In fact, all the orbits would stay exactly as they are now. Nothing would happen to us apart from freezing to death. If we wanted to study a black hole, we could put a probe in orbit around it the same way we put probes around other astronomical bodies. It's not going to instantly spiral to its doom (at least not any faster than it would around anything else), and in fact since a black hole without matter actively falling on it would emit just that feeble Hawking radiation and is much smaller than a star or another body of similar mass such probe could orbit close to it, tidal forces aside, even if such close orbit could need a lot of energy to depart it.

Another common misconception is that all the stars in the galaxy orbit the supermassive black hole at the center, the same way all the objects in the solar system orbit the Sun. However, the Sun makes up 99.8 percent of the mass of the solar system, while the supermassive black hole at the center of our galaxy (Sagittarius A*), despite having the equivalent of 4.5 million solar masses, is only 0.0001 percent of the total mass of the galaxy. Sagittarius A* therefore cannot be solely or even mainly responsible for the orbits of all the stars in the galaxy. If it were removed, almost nothing would change. Strictly speaking, everything in our galaxy does not orbit the supermassive black hole at the center, but rather orbits the center of mass of the galaxy, which includes the supermassive black hole (and which happens to be at the center), but also includes the tens of millions of stars also clustered around the middle. The galactic orbital paths of all objects in the galaxy are caused by the total mass of the galaxy, not solely the mass of the black hole at the center. ^note This is actually true of all orbits. Smaller objects do not actually orbit larger objects, but rather both orbit their combined center of mass, called the barycenter. If one object is significantly more massive than the other, that barycenter may be near or below the surface of the more massive object, but it will not be located at its exact center. For example, the center of mass of the solar system is not actually the very center of the Sun, but is a point which is constantly changing - sometimes even being located outside the surface of the Sun. And yes, this means the orbital paths of all the planets are also constantly changing. Not by much, but it's measurable. Likewise, the supermassive black hole Sagittarius A* is located very near the galactic rotational center, but is not exactly at the center.

Unless you're watching extremely hard Sci-Fi, a black hole is probably nothing like you've generally seen in fiction. Black holes rank up there with FTL and Time Travel as one of the most frequently exploited bits of science.

How can you exit a black hole?

So, you survived the massive radiation poisoning, and the spaghettification, and you're past the event horizon and you haven't died yet. And now you want to go home? Wow, you really dream big!

The event horizon is not a thing but a location where your escape velocity is a speed faster than 300,000 kilometres per second (the speed of light). That escape velocity itself can vary, depending on the mass of the black hole or how deep you are. It's perfectly possible that at some point past the event horizon, the escape velocity is twice the speed of light.^note Upon entering a black hole, all future paths you could possibly take lead towards the singularity. In addition, time slows to a complete halt for you, relative to an outside observer, who can somehow see through an event horizon. This means that an infinite amount of time would pass outside the black hole, for each instant that you are inside the black hole. Theoretically you could make the black hole's escape velocity if you had a magical Faster Than Lightspeed ship, but in keeping with the rule that the faster something moves, the slower it ages, this would result in time rewinding for everything going FTL — the ship and its instruments as well as any people inside it. This would mean you could time-travel back to before you entered the black hole, thus "escaping" it. There are several quasi-logical outcomes of trying this (amid millions of other possibilities). Of course, since time travel is another of those things that spits in the eye of physics, these are all wild guesses:

1. You just fry yourself with the concentrated beam of blueshifted gamma-rays you made by screwing with relativistic speeds, which happens before you even break c. This is the most likely outcome. Happy dying!
2. If you perhaps manage to break light-speed, the atoms in your body and your ship disintegrate into your component particles anyway. You are dead.
3. You reverse yourself in time, but fail to move in space. You think you are outside the black hole, and so does your magical FTL ship, but you're not. Eventually you hit the singularity and disintegrate, but you don't even notice. You are dead.
4. You successfully reverse only yourself to a point and place in time before entering the black hole without changing everything else. You appear outside the hole, perhaps in your partner's ship. However your memories are reversed, but the universe outside continues. Your interactions with the world return through the events you rewound, regardless of the input your brain should be receiving. You are now more like a broken record than a human being. The world, while sad that a great mind has been forever lost, is grateful to your now institutionalised person for your research.
5. You reverse the history of the universe to before you entered the black hole. Everything, including your ship's instruments and your memories of everything that happened before that point, has reversed to that point. Not remembering that you have been into the black hole before, you enter it again like an idiot... and then again... and again. You have just doomed the entire universe to exist as a broken record, but nobody ever notices. Nice going.
6. You appear outside the black hole with your memories and the recordings of your ship intact. Congratulations! You just rewound the entire history of the universe except yourself! So you don't go in again. Then a collection of paradoxes gangs up on you asking unpleasant questions like how you can have information about the black hole if you didn't go in. Your impossible presence causes the universe to disintegrate, implode, or just switch off instantly like a light-bulb.
7. You only manage to kill yourself faster because space beyond the event horizon has warped by the gravitational forces to the point the only direction you can move is further in. At best you can manage to stay in place long enough for the black hole to dissipate on its own and you might live long enough to do so since time is moving extra slow for you. A lot of time will have passed for everyone not breaking light speed barriers beyond event horizons. ^note See page quote for an alternate possibility.
8. The desired scenario: you appear outside the black hole with full memory of your experience and data in hand, you don't go in again, and the universe somehow doesn't switch off. Congratulations, not only have you rewound the entire universe except yourself, defying all laws of physics, but you have defied all possible logic too. You are now God, or possibly the Doctor.

However, this is all a moot point. FTL travel is impossible (at least, based on all the numbers and laws and theories and quantum we currently possess) and so you can't have yourself a magical FTL-speed ship anyway.^note Fortunately, since FTL ships don't exist you're not going to be able to go anywhere near a black hole anyway. Because if you could, you might as well click your heels together three times and wish your way out.

In fact, it's been noted that black holes are nature's way of dividing by zero. Have fun arguing with infinity.

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