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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
Inside the event horizon of a black hole, there is no way out. There are no directions of space that point away from the singularity. Due to the Lovecraftian curvature of spacetime within the event horizon, all the trajectories that would carry you away from the black hole now point into the past.And it is getting closer.
In fact, this is the definition of the event horizon. It's the boundary separating points in space where there are trajectories that point away from the black hole from points in space where there are none.
Your magical infinitely-accelerating engine is of no use to you...because you cannot find a direction in which to point it. The singularity is all around you, in every direction you look.
A black hole is, quite literally, a Swirly Energy Thingy (okay, rotation is technically optional, but most natural black holes probably do spin). A point of space so massive that even objects going at the speed of light (for example: light itself) cannot escape its gravity (thus its name). This phenomenon has fascinated scientists and writers of fiction for many, many years.
Black holes are collapsed stars, but not many people know why the stars have collapsed in such a way to create black holes. To find out we'll have to look at how stars evolve, for they can end in one of three ways: a black dwarf, a neutron star, or a black hole.
Stars convert hydrogen into helium via fusion. Heat is the kinetic energy of moving particles, so make it hot enough and hydrogen nuclei will move at such speed that they have no time to repel each other with electromagnetic repulsion. When they collide, they are able to fuse together thanks to the "strong force", releasing an enormous amount of energy and creating helium. On Earth, this takes a Tokamak reactor and billions of dollars; in space, all it takes is a few hundred septillion tons of hydrogen. A main-sequence star like our Sun is in a constant balancing act, where the fusion at its core produces energy, pushing outward against gravity, and preventing the outer non-fusing layers from collapsing in on the core to form "degenerate matter" (the stuff you hear about when someone starts talking about something weighing a mountain per teaspoonful or the like).
As the star ages, it exhausts its hydrogen supply by converting it into helium. However, the star will continue to live, as its core collapses inward on itself further, increasing the pressure and temperature at the core. Eventually, the core becomes hot enough that helium starts to fuse into heavier elements such as carbon and then oxygen. During the short period where the core is pure helium, the shell of the star, which continues to fuse hydrogen, gains enough kinetic energy to expand away from the star, becoming the outer layers of a red giant. Once the star contains a core of pure iron, however, the star's life is at its end. The cold math of hot fusion tells us that fusion releases energy only up to iron; beyond that it requires an input of energy, and a small star doesn't have the gravitational oomph necessary to provide that input. The outer layers are shed off as a planetary nebula after the core becomes solid iron. No longer supported by fusion, the exposed core of the star condenses into a degenerate-matter white dwarf which slowly cools over trillions of years into a black dwarf only a fraction of a degree above absolute zero.
(Incidentally, current theory indicates low-mass red dwarfs don't go through the giant stage because their outer layers are more efficiently mixed into the fusing core; it's believed they will become brighter "blue dwarfs" before settling into the inert white dwarf stage. This hasn't been verified by observation as the universe hasn't been around for the hundreds of billions of years necessary for those stars to reach that point.)
But that's only for mid-sized stars. For more massive stars, the core is bigger and thus this process starts much earlier. Following the exhaustion of hydrogen and the fusing of iron in the star core, the star (which from the outside is now a red supergiant as big as Jupiter's orbit) has an onion-like core of shells made up of the first twenty-five elements of the periodic table. The star's core becomes so hot that even those elements start to combine -- but because the binding energies of the nuclei of all elements following iron decrease successively, further fusion results in the loss of energy, rather than the release, so even as the core starts making serious elements like gold, bismuth and uranium, it can't support its own weight and collapses further, taking in more mass. If the star's mass was greater than the Chandrasekhar limit (1.4 solar masses), electron degeneracy pressure breaks down completely because gravity merges electrons and protons together to form neutrons and the neutron star is born from dying star's core, when outer layers are blown away. The neutron star is held up against its weight by the neutron degeneracy pressure (notice a theme here?). But if the core exceeds the Tolman-Oppenheimer-Volkoff limit (about two to three solar masses, and definitely no more than five, but it's still unclear), neutron degeneracy pressure will break down as well and neutrons are merged. What should happen with matter in such case is uncertain, but the size of heavy neutron star is already close to that of black holes of same mass and so it can be assumed, that resulting object collapse below event horizon and gravity condenses the core down to a point in space that is infinitely small, yet immensely massive and infinitely dense (Density is, after all, mass divided by volume), called a singularity, similar to the theoretical beginning state of the universe in the Big Bang Theory. So small and so massive, not even light can escape. Or it should if initial mass was not rotating. However, it is not the case and usually a rotating black hole is formed, that is even more alien.
Black holes are strange things. Besides the singularity at the center, there is the event horizon, the point of no return, that once you cross it...you can't 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. Rotating black holes also have ergosphere: a region near event horizon, where space-time spin around black holes faster then light.
In fact, space-time will become quite freaky around the event horizon: the closer you get to the event horizon, the slower time becomes (due to relativity, however, 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 stop (nobody would actually see you hit the event horizon, since you appear to slow down as you get closer, for an outside observer, you would take an infinite amount of time to reach it. You wouldn't actually stop, that's just what they'll see). This prediction, however, assumes zero mass of incoming object and neglect 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 would just continue accelerating until you hit the singularity and are compacted into it.
However, you'd probably be long dead before that anyway as black holes come with some dangers attached due to the extremely intense gravity around them: 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. 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. It's known as inflationary instability and, according to scientists, its effects would go very far beyond of just vaporizing your body.
Black holes normally can't be seen (thus their moniker), but there are ways they are visible: if they are near another star and siphoning off mass, they can form accretion disks, which glow hot. There's gravitation lensing, in which black holes are detected by the image distortions of objects behind them (The Other Wiki has a nice animation for that here). And then there's Hawking radiation, which basically is a way for black holes to radiate stuff (by quantum mechanics), and is a whole other can of non-zero entropy worms. One of its more practically relevant attributes is that a black hole loses mass/energy this way -- 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 sun-mass black hole, on the other hand, would lose about a milligram of its mass-energy every 3.1 x 1031 (31 nonillion) years. 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). Think of it like this: In the same way that a solar system is a large central star with many planets and other celestial objects orbiting it, a galaxy is a supermassive black hole with stars and their solar systems orbiting around it, albeit on an even grander scale, relatively speaking.
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.
Another useful note is that black holes are one of 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. So 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.
Right now there's 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.
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 ("Schwarzchild") black hole has a surprisingly straightforward formula:
RSchwarzchild = 3 km * mass in Solar masses
And 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.
A black hole with 4 million solar masses, such as the black hole theorized 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.
Going even further, the largest known black hole in the nearby Universe -the one located in the center of the giant elliptical galaxy M87 that has an estimated mass of 6.4 billion solar masses- would have a radius of 19.2 billion km, larger than our Solar System.
The odd thing about this, when compared with most "normal" spherically-shaped objects in the universe, is that a black hole's diameter is directly proportional to its mass -- double the Schwarzchild 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. 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.
- ↑ Not to be confused with "brown dwarfs", which are substellar bodies that were never massive enough to sustain fusion to begin with.
- ↑ electrons of the same spin cannot occupy the same space; this prevents matter from collapsing, unless gravity is really kicking matter's ass
- ↑ When discussing the density of the entire region inside the event horizon, not the density of the singularity at the center.