What is a black hole?

Loosely speaking, a black hole is a region of space that has so much mass concentrated in it that there is no way for a nearby object to escape its gravitational pull. Since our best theory of gravity at the moment is Einstein's general theory of relativity, we have to delve into some results of this theory to understand black holes in detail, but let's start of slow, by thinking about gravity under fairly simple circumstances.

Suppose that you are standing on the surface of a planet. You throw a rock straight up into the air. Assuming you don't throw it too hard, it will rise for a while, but eventually the acceleration due to the planet's gravity will make it start to fall down again. If you threw the rock hard enough, though, you could make it escape the planet's gravity entirely. It would keep on rising forever. The speed with which you need to throw the rock in order that it just barely escapes the planet's gravity is called the "escape velocity." As you would expect, the escape velocity depends on the mass of the planet: if the planet is extremely massive, then its gravity is very strong, and the escape velocity is high. A lighter planet would have a smaller escape velocity. The escape velocity also depends on how far you are from the planet's center: the closer you are, the higher the escape velocity. The Earth's escape velocity is 11.2 kilometers per second (about 25,000 m.p.h.), while the Moon's is only 2.4 kilometers per second (about 5300 m.p.h.).

Now imagine an object with such an enormous concentration of mass in such a small radius that its escape velocity was greater than the velocity of light. Then, since nothing can go faster than light, nothing can escape the object's gravitational field. Even a beam of light would be pulled back by gravity and would be unable to escape.

The idea of a mass concentration so dense that even light would be trapped goes all the way back to Laplace in the 18th century. Almost immediately after Einstein developed general relativity, Karl Schwarzschild discovered a mathematical solution to the equations of the theory that described such an object. It was only much later, with the work of such people as Oppenheimer, Volkoff, and Snyder in the 1930's, that people thought seriously about the possibility that such objects might actually exist in the Universe. (Yes, this is the same Oppenheimer who ran the Manhattan Project.) These researchers showed that when a sufficiently massive star runs out of fuel, it is unable to support itself against its own gravitational pull, and it should collapse into a black hole.

In general relativity, gravity is a manifestation of the curvature of spacetime. Massive objects distort space and time, so that the usual rules of geometry don't apply anymore. Near a black hole, this distortion of space is extremely severe and causes black holes to have some very strange properties. In particular, a black hole has something called an 'event horizon.' This is a spherical surface that marks the boundary of the black hole. You can pass in through the horizon, but you can't get back out. In fact, once you've crossed the horizon, you're doomed to move inexorably closer and closer to the 'singularity' at the center of the black hole.

You can think of the horizon as the place where the escape velocity equals the velocity of light. Outside of the horizon, the escape velocity is less than the speed of light, so if you fire your rockets hard enough, you can give yourself enough energy to get away. But if you find yourself inside the horizon, then no matter how powerful your rockets are, you can't escape.

The horizon has some very strange geometrical properties. To an observer who is sitting still somewhere far away from the black hole, the horizon seems to be a nice, static, unmoving spherical surface. But once you get close to the horizon, you realize that it has a very large velocity. In fact, it is moving outward at the speed of light! That explains why it is easy to cross the horizon in the inward direction, but impossible to get back out. Since the horizon is moving out at the speed of light, in order to escape back across it, you would have to travel faster than light. You can't go faster than light, and so you can't escape from the black hole.

(If all of this sounds very strange, don't worry. It is strange. The horizon is in a certain sense sitting still, but in another sense it is flying out at the speed of light. It's a bit like Alice in "Through the Looking-Glass": she has to run as fast as she can just to stay in one place.)

Once you're inside of the horizon, spacetime is distorted so much that the coordinates describing radial distance and time switch roles. That is, "r", the coordinate that describes how far away you are from the center, is a timelike coordinate, and "t" is a spacelike one. One consequence of this is that you can't stop yourself from moving to smaller and smaller values of r, just as under ordinary circumstances you can't avoid moving towards the future (that is, towards larger and larger values of t). Eventually, you're bound to hit the singularity at r = 0. You might try to avoid it by firing your rockets, but it's futile: no matter which direction you run, you can't avoid your future. Trying to avoid the center of a black hole once you've crossed the horizon is just like trying to avoid next Thursday.

Incidentally, the name 'black hole' was invented by John Archibald Wheeler, and seems to have stuck because it was much catchier than previous names. Before Wheeler came along, these objects were often referred to as 'frozen stars.' 

What would happen to me if I fell into a black hole?
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Let's suppose that you get into your spaceship and point it straight towards the million-solar-mass black hole in the center of our galaxy. (Actually, there's some debate about whether our galaxy contains a central black hole, but let's assume it does for the moment.) Starting from a long way away from the black hole, you just turn off your rockets and coast in. What happens?

At first, you don't feel any gravitational forces at all. Since you're in free fall, every part of your body and your spaceship is being pulled in the same way, and so you feel weightless. (This is exactly the same thing that happens to astronauts in Earth orbit: even though both astronauts and space shuttle are being pulled by the Earth's gravity, they don't feel any gravitational force because everything is being pulled in exactly the same way.) As you get closer and closer to the center of the hole, though, you start to feel "tidal" gravitational forces. Imagine that your feet are closer to the center than your head. The gravitational pull gets stronger as you get closer to the center of the hole, so your feet feel a stronger pull than your head does. As a result you feel "stretched." (This force is called a tidal force because it is exactly like the forces that cause tides on earth.) These tidal forces get more and more intense as you get closer to the center, and eventually they will rip you apart.

For a very large black hole like the one you're falling into, the tidal forces are not really noticeable until you get within about 600,000 kilometers of the center. Note that this is after you've crossed the horizon. If you were falling into a smaller black hole, say one that weighed as much as the Sun, tidal forces would start to make you quite uncomfortable when you were about 6000 kilometers away from the center, and you would have been torn apart by them long before you crossed the horizon. (That's why we decided to let you jump into a big black hole instead of a small one: we wanted you to survive at least until you got inside.)

What do you see as you are falling in? Surprisingly, you don't necessarily see anything particularly interesting. Images of faraway objects may be distorted in strange ways, since the black hole's gravity bends light, but that's about it. In particular, nothing special happens at the moment when you cross the horizon. Even after you've crossed the horizon, you can still see things on the outside: after all, the light from the things on the outside can still reach you. No one on the outside can see you, of course, since the light from you can't escape past the horizon.

How long does the whole process take? Well, of course, it depends on how far away you start from. Let's say you start at rest from a point whose distance from the singularity is ten times the black hole's radius. Then for a million-solar-mass black hole, it takes you about 8 minutes to reach the horizon. Once you've gotten that far, it takes you only another seven seconds to hit the singularity. By the way, this time scales with the size of the black hole, so if you'd jumped into a smaller black hole, your time of death would be that much sooner.

Once you've crossed the horizon, in your remaining seven seconds, you might panic and start to fire your rockets in a desperate attempt to avoid the singularity. Unfortunately, it's hopeless, since the singularity lies in your future, and there's no way to avoid your future. In fact, the harder you fire your rockets, the sooner you hit the singularity. It's best just to sit back and enjoy the ride.

My friend is sitting still at a safe distance, watching me fall into the black hole. What does she see?

Penelope sees things quite differently from you. As you get closer and closer to the horizon, she sees you move more and more slowly. In fact, no matter how long she waits, she will never quite see you reach the horizon.

In fact, more or less the same thing can be said about the material that formed the black hole in the first place. Suppose that the black hole formed from a collapsing star. As the material that is to form the black hole collapses, Penelope sees it get smaller and smaller, approaching but never quite reaching its Schwarzschild radius. This is why black holes were originally called frozen stars: because they seem to 'freeze' at a size just slightly bigger than the Schwarzschild radius.

Why does she see things this way? The best way to think about it is that it's really just an optical illusion. It doesn't really take an infinite amount of time for the black hole to form, and it doesn't really take an infinite amount of time for you to cross the horizon. (If you don't believe me, just try jumping in! You'll be across the horizon in eight minutes, and crushed to death mere seconds later.) As you get closer and closer to the horizon, the light that you're emitting takes longer and longer to climb back out to reach Penelope. In fact, the radiation you emit right as you cross the horizon will hover right there at the horizon forever and never reach her. You've long since passed through the horizon, but the light signal telling her that won't reach her for an infinitely long time.

There is another way to look at this whole business. In a sense, time really does pass more slowly near the horizon than it does far away. Suppose you take your spaceship and ride down to a point just outside the horizon, and then just hover there for a while (burning enormous amounts of fuel to keep yourself from falling in). Then you fly back out and rejoin Penelope. You will find that she has aged much more than you during the whole process; time passed more slowly for you than it did for her.

So which of these two explanation (the optical-illusion one or the time-slowing-down one) is really right? The answer depends on what system of coordinates you use to describe the black hole. According to the usual system of coordinates, called "Schwarzschild coordinates," you cross the horizon when the time coordinate t is infinity. So in these coordinates it really does take you infinite time to cross the horizon. But the reason for that is that Schwarzschild coordinates provide a highly distorted view of what's going on near the horizon. In fact, right at the horizon the coordinates are infinitely distorted (or, to use the standard terminology, "singular"). If you choose to use coordinates that are not singular near the horizon, then you find that the time when you cross the horizon is indeed finite, but the time when Penelope sees you cross the horizon is infinite. It took the radiation an infinite amount of time to reach her. In fact, though, you're allowed to use either coordinate system, and so both explanations are valid. They're just different ways of saying the same thing.

In practice, you will actually become invisible to Penelope before too much time has passed. For one thing, light is "redshifted" to longer wavelengths as it rises away from the black hole. So if you are emitting visible light at some particular wavelength, Penelope will see light at some longer wavelength. The wavelengths get longer and longer as you get closer and closer to the horizon. Eventually, it won't be visible light at all: it will be infrared radiation, then radio waves. At some point the wavelengths will be so long that she'll be unable to observe them. Furthermore, remember that light is emitted in individual packets called photons. Suppose you are emitting photons as you fall past the horizon. At some point, you will emit your last photon before you cross the horizon. That photon will reach Penelope at some finite time -- typically less than an hour for that million-solar-mass black hole -- and after that she'll never be able to see you again. (After all, none of the photons you emit *after* you cross the horizon will ever get to her.)

Where can I go to learn more about black holes?

Let me begin by acknowledging that I cribbed some of the above material from the article about black holes in the Frequently Asked Questions list for the Usenet newsgroup sci.physics. The sci.physics FAQ is posted monthly to sci.physics and is also available by anonymous ftp from rtfm.mit.edu (and probably other places). The article about black holes, which is excellent, was written by Matt McIrvin. The FAQ contains other neat things too.