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.
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.
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.
Just click on the pictures above for a better view!
You can't see a black hole directly, of course, since light can't get past the horizon. That means that we have to rely on indirect evidence that black holes exist.
Suppose you have found a region of space where you think there might be a black hole. How can you check whether there is one or not? The first thing you'd like to do is measure how much mass there is in that region. If you've found a large mass concentrated in a small volume, and if the mass is dark, then it's a good guess that there's a black hole there.
According to a recent review by Kormendy and Richstone (to appear in the 1995 edition of "Annual Reviews of Astronomy and Astrophysics"), eight galaxies have been observed to contain such massive dark objects in their centers. The masses of the cores of these galaxies range from one million to several billion times the mass of the Sun. The mass is measured by observing the speed with which stars and gas orbit around the center of the galaxy: the faster the orbital speeds, the stronger the gravitational force required to hold the stars and gas in their orbits.
Two very recent discovery has been made that strongly support the hypothesis that these systems do indeed contain black holes. First, a nearby active galaxy was found to have a "water maser" system (a very powerful source of microwave radiation) near its nucleus. Using the technique of very-long-baseline interferometry, a group of researchers was able to map the velocity distribution of the gas with very fine resolution. In fact, they were able to measure the velocity within less than half a light-year of the center of the galaxy. From this measurement they can conclude that the massive object at the center of this galaxy is less than half a light-year in radius. It is hard to imagine anything other than a black hole that could have so much mass concentrated in such a small volume. (This result was reported by Miyoshi et al. in the 12 January 1995 issue of Nature, vol. 373, p. 127.)
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