Astronomy 162: Professor Barbara Ryden
An object with infinite density is distressing to think about (it was bad enough contemplating a neutron star with a density of 400 million tons per cubic centimeter!) Fortunately for the sanity of astronomers, it is impossible to see a singularity, because its escape speed is too high.
The escape speed V at a distance R from a mass M is given
by the formula:
V = ( 2 G M / R )1/2 ,
where G is Newton's gravitational constant. For instance, at the surface of the Sun (whose mass is 2 x 1030 kilograms), you are at a distance R = 700,000 kilometers from the Sun's center. The escape speed from the Sun's surface can be computed to be V = 620 kilometers/second. At R = 1 AU = 150,000,000 kilometers from the Sun's center, the escape speed from the Sun is only V = 42 kilometers/second. The farther you get from a massive object, the lower the escape speed is.
At a very great distance from a singularity of mass M, the escape speed is tiny. As you approach the singularity, however, and R steadily decreases, the escape speed V becomes higher and higher. At a critical radius, known as the Schwarzschild radius, the escape speed becomes equal to the speed of light.
The numerical value of the Schwarzschild radius, Rs,
is given by the equation:
where G is Newton's gravitational constant, and c is the speed of light. In practical units,
Rs = 3 kilometers ( M / 1 Msun )
In other words, a singularity with a mass equal to that of the Sun will have a Schwarzschild radius of only 3 kilometers. The Schwarzschild radius is directly proportional to the mass of a singularity.
A black hole is defined as ANY object which is smaller than its Schwarzschild radius. For instance, take an astronomy professor with a mass of M = 70 kilograms. Squeeze her down to a sphere with radius R = 10-25 meters, and she will be a black hole.
In theory, a black hole can have any mass; take an object of any size and squeeze it down to its Schwarzschild radius - instant black hole. The collapse of massive stars is merely a convenient means of making black holes with masses of M = 3-10 Msun and Schwarzschild radii of Rs = 9-30 kilometers.
A black hole can be thought of as a Cosmic Lobster Trap; objects can enter the event horizon easily enough, but nothing (not even light) can come out. Here in the outside universe, we have no information whatsoever about what is going on inside an event horizon. We presume that once a dense stellar core is compressed into a black hole, it goes on to become a singularity; that is what the laws of physics predict. However, we have no way of confirming this prediction by observation from outside the event horizon. If you entered the event horizon, you would be able to discover whether there's a singularity inside. However, you wouldn't be able to communicate your results to anyone outside the event horizon. Information cannot travel from inside an event horizon to outside an event horizon.
In cheap science fiction stories, black holes are sometimes described as if they are ``cosmic vacuum cleaners'', sucking up everything in their path with the malevolent force of their gravity. Black holes are much more benign than that. Black holes are inescapable only if you venture inside the event horizon. The event horizon of a black hole which forms from a collapsing star is quite small - only 10 miles or so in radius.
Suppose you are orbiting a black hole at a safe distance (well outside the event horizon). Unwilling to make the one-way trip inside the event horizon yourself, you drop a warthog - snout first - toward the black hole, after tying a to the warthog's tail. As the warthog drops toward the event horizon, what happens? Well, as frequently happens in life, what you see depends on where you are.
Unfortunately, as the warthog approaches the singularity, it will be ripped apart by incredibly strong tidal forces. The gravitational pull on its snout will be much stronger than the pull on its rump, and it will be shredded. (The ASPCA would definitely not approve of this experiment...)
Updated: 2003 Feb 12
Copyright © 2003, Barbara Ryden