If the initial mass of a star is greater than 20 Msun or so, its supernova explosion leaves behind a dense core with M > 3 Msun. Since it is too massive to become a neutron star, the dense core collapses totally. Nothing can stop its infall; according to the laws of physics, taken to their logical conclusion, it becomes a singularity. A singularity is a point which has zero radius and infinite density.
An object with infinite density is distressing to think about (it was bad enough contemplating a neutron star with a density of 100 million tons per cubic centimeter!) Fortunately for the sanity of astronomers, it is impossible to see a singularity, because its escape velocity is too high.
The escape velocity 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, we are
at a distance R = 6400 kilometers from the center of the earth,
which has a mass M = 6 x 1021 tons. Work out the
escape velocity from the surface of the Earth, and it turns out
to be V = 11 kilometers/second. Toss something straight up into
the air with a speed of 11 km/sec, and it will escape the Earth's
gravitational pull.
At a very great distance from a singularity of mass M, the escape velocity is tiny. As you approach the singularity, however, and R steadily decreases, the escape velocity V becomes higher and higher. At some critical radius, known as the Schwarzschild radius, the escape velocity 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.
Draw a sphere of radius Rs around a singularity. This sphere is known as the event horizon. Inside the event horizon, the escape velocity from a singularity is greater than the speed of light. Since nothing can travel faster than the speed of light, nothing can escape from inside the event horizon.
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. If the dense core, once it is compressed within the event horizon, suddenly turns into a flock of enormous cosmic flamingoes, we simply would have no way of knowing. 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.
For instance, if the Sun were squeezed down into a black hole, what would happen to the Earth's orbit? Would it start a death spiral inward, drawn inexorably onward by the black hole's unescapable gravity? NOT!! The Earth's orbit would remain unchanged. Gravitational force depends only on the MASS of objects involved and the DISTANCE between them. The gravitational attraction between the Earth and Sun will be the same as long as the masses and distances remain constant. It doesn't matter whether the Sun is a black hole or a sphere of hydrogen and helium or a lump of peanut butter, as long as the mass is the same.
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.
Close to the event horizon of a black hole,
space and time are strongly warped, according to the tenets of
General Relativity. Let us examine a few of the more
mind-boggling relativistic effects by taking an imaginary
Journey into a Black Hole.
Suppose you are orbiting a black hole at a safe distance (well outside the event horizon). You drop a friend - feet first - toward the black hole, after handing him a to use as a beacon to mark his progress. As your friend drops toward the event horizon, what happens? Well, as frequently happens in life, what you see depends on where you are.
As your friend approaches the event horizon, you see:
Eventually, in the far distant future, your descendents will see a faint, ghostly image of your friend, moving excruciatingly slowly, never quite reaching the event horizon.
As your friend approaches the event horizon, he sees:
In short, your friend sees nothing unusual in his immediate vicinity. He passes through the event horizon with nothing unusual happening to mark the boundary crossing.
Unfortunately, as he approaches the singularity, your friend will be ripped apart by incredibly strong tidal forces. The gravitational pull on his feet will be much stronger than the pull on his head and he will be shredded. (So don't try this experiment with a REALLY close friend.)
Suppose you want to locate a black hole (perhaps you want to drop an enemy into it). How can you detect something which is - by definition - totally black, with no electromagnetic radiation emerging from it at all? We can only detect a black hole indirectly, by observing the effect it has on matter which is just outside its event horizon.
A black hole in a close binary system will have gas dumped onto it by its stellar companion. As the gas approaches the event horizon, it will be heated by the strong tidal forces, and start to emit X-rays. One way of detecting black holes, then, is to look for binary systems which are strong X-ray sources. Using Kepler's Third Law, compute the mass of the compact object onto which the gas is being dumped. If its mass is greater than 3 Msun, it must be a black hole instead of a neutron star.
The X-ray source known as Cygnus X-1, for instance, is a binary system with a period of 5.6 days. The normal star in the system is a supergiant star of spectral type O. If the mass of the normal star is 30 Msun (normal for a blue supergiant) then its compact companion must have a mass of 6 to 11 Msun, well above the upper limit for neutron stars. Other X-ray binary systems are known whose compact members are too massive to be neutron stars.
Ultramassive black holes are also suspected to exist in the centers of galaxies. Observe the orbital motions of gas and stars about the center of a galaxy; then, using Kepler's Third Law, you can deduce the mass of the central object (if it exists). Analysis of the center of our galaxy, for instance, reveals the presence of a dark object with a mass of 2 million Msun. Similar analysis of our neighbor the Andromeda Galaxy reveals the presence of a central dark object with a mass of 30 million Msun. These central objects are so compact, dim, and massive, they must be black holes.
The Hubble Space Telescope is a useful tool for
ferreting out black holes in the centers of galaxies.
The above picture shows the center of the galaxy NGC 4261, which
is located 100 million light years away, in the constellation
Virgo. (Click on the image for an enlarged view.) What you are
looking at is a gaseous disk 400 light years in radius, rotating
around a central black hole. The measured velocity of the
rotating gas, when plugged into Kepler's Third Law, indicates
that the mass of the black hole must be 1.2 Billion Msun.
(Image credit: Laura Ferrarese [Johns Hopkins U.] and NASA)
