Tom Jonard's Black Hole Page
Most of the following was originally written for a friend as an elementary and non-technical introduction to black holes.
What is a Black Hole?
Some black holes are a kind of dead star. At least theory suggests that some stars might become black holes when they die. It is difficult to confirm this theory because black holes should emit no light or radiation of any kind, which is the primary means by which we observe astronomical objects. Hence the name. The actual existence of black holes can only be confirmed from observations of their effects on something else.To understand black holes you need lots of background information. They are esoteric, weird and the laws of nature that apply to them are not those familiar to the inhabitants of normal space and time. The story of how the theory of black holes developed is worth knowing in itself and you can read about it in Kip Thorn's Black Holes and Time Warps (W.W. Norton & Company, 1994).
Gravity
The first thing you need to know is something about gravity. Gravity is the weakest of all the fundamental forces of nature about which we know. But it acts between every particle of matter in the universe attracting it to every other particle. Its range is infinite and it is always attractive. Normally we think of gravity only as the force which holds us on the earth. But gravity also acts between you and me pulling us together. It is so weak that we do not notice this but it could be measured. We are also attracted to every other particle of matter in the universe but the force is so weak because it falls off with the square of the distance that we could not even measure it.Astrology maintains that the planets influence us, but if true it cannot be through gravity since the attraction of people and ordinary objects around us is vastly greater than that of the planets. Of course they have a bit of the truth because we are attracted to every body (and particle) in the universe (not just the planets).
To understand the weakness of gravity think of another force -- electromagnetism. An ordinary refrigerator magnet is able to defy gravity for its own mass and that of a few pieces of paper. A stronger magnet could hold a toaster to your refrigerator. An electrostatic charge is able to do the same for bits of paper and dust, causing them to stick to your clothing. If you and I were charged sufficiently we might be attracted (or repulsed) with an irresistible force (far stronger than our mutual gravitational attraction) until we contacted and discharged.
Therein lies another difference with gravity -- electrical charges are positive and negative and can be attractive and repulsive (different charges attract and like repel). We normally are not attracted or repelled by electrostatic force because our individual positive and negative charges (consisting of charged particles) balance out. There is no such cancellation for gravity. It always attracts and it attracts everything.
By the way, herein lies a major cosmological puzzle, first realized by Newton after he formulated his theory of gravity. If everything in the universe attracts why hasn't all the material in the universe fallen together under this attraction into a ball? Either it has not had time to do so, or the universe is not infinite (if it were the infinite gravity would cause it to collapse in an instant!). It does not even seem that the universe is collapsing (back then they did not know it was expanding which at least solves the puzzle for the time being).
The Life of a Star
The life of a star is basically a story of collapse under the force of gravity delayed by thermonuclear reaction. (I bet you didn't think we were going to ever get back to the main story did you?).A cloud of mostly hydrogen gas in deep space collapses under its own gravity to form a spherical object we call a star (more or less, how collapse is initiated and proceeds is very complicated in reality). The overlying gas in the star presses down on the central core. The pressure is caused by the mutual gravitational attraction of every particle in the star for every other. As the pressure rises so does the temperature. This is according to the laws of thermodynamics. If you have ever pumped up a bicycle tire you might have noticed how the end of the pump and the attachment to the tire get warm and sometimes hot. Whenever you increase pressure on matter you will cause its temperature to rise.
When the temperature in the core reaches about 10 million degrees a thermonuclear reaction begins. This reaction causes hydrogen to be converted into helium. For every 2 atoms of hydrogen one atom of helium is produced. The one atom of helium is slightly less massive than the sum of the masses of the 2 hydrogen atoms. The missing mass is converted into energy as described by the famous equation
e = mc2where e = energy, m = mass and c = the Speed of Light which is squared. The square of the Speed of Light (300,000 kps) is a truly large number (90,000,000,000) guaranteeing that even the small amount of mass lost in the reaction produces a prodigious amount of energy. Essentially the core of the star becomes a continuously operating thermonuclear bomb.
In the weak gravity at the surface of the earth about the only thing you can do with a thermonuclear bomb is blow up things (like cities). But in the core of a star the explosion is contained by the overlying gravitationally bound gas. The outward pressure of the explosion (which is by the way far greater than anything people have ever done) is balanced by the inward gas pressure. This can go on for billions of years.
But it can't go on forever. Eventually the hydrogen fuel will run out. Then the star starts to collapse again. The core temperature continues to rise. Eventually it will rise until a new thermonuclear reaction starts. Now helium will be fused into carbon. Since this reaction is hotter more energy is radiating from the core and the overlying gas of the star is pushed out and it becomes a red giant. This can go on for a 100,000 years.
But it can't go on forever. Eventually the helium fuel will run out. You can probably guess where this is going. There are a series of thermonuclear reactions that can occur in the core fusing lighter elements into heavier. Each cycle is hotter. And shorter. Until the core has produced iron. Iron can be fused to produce heavier elements, but there is a catch. Instead of producing energy it requires the input of energy. When the core has converted all its mass into iron it has reached the end of energy production. Without energy from the core there is nothing to continue to delay the collapse of the star. And so it collapses and dies.
There are a number of simplifications above. One is that hydrogen is always being converted somewhere in the star. Just not in the core. Same thing for helium once helium fusion has started. And so forth.
The Death of a Star
What happens to the star next depends on its mass. An average star like the sun will collapse into an object known as a white dwarf. These are incredibly dense objects a few thousand miles in diameter. A teaspoon of matter from a white dwarf would weight about 10 million tons. They are white hot initially because of the heat of compression that results in the collapse. Over a long time they cool to dark cinders. White dwarfs do not collapse further because to do so electrons and neutrons in their matter would have to merge together. The gravitational force force felt by these particles is not enough to overcome the quantum forces that prevent this.Normal matter consists of 99.999999% empty space. Most of the mass of a normal atom is contained in an incredibly small nucleus. Electrons occupy a relatively vast shell around this nucleus and electro-magnetic forces keep the atoms apart. In the matter of a white dwarf (called degenerate state matter) all the space normally occupied by the electrons has been "squeezed out".
But theory says that if stars are more massive than about 1.5 times the sun something else should happen. (Notice that we have jumped into theory. White dwarfs were discovered observationally and then explained. Now we are going to talk about things that scientists first thought might happen and then were actually found later.) At this size the gravitational attraction of all that mass should be enough to compress matter further. And it does. Above this limit the repulsive forces are not enough to keep the electrons out of the nuclear particles. They combine with the protons to form neutrons. The result is a neutron star. A teaspoon of matter from a neutron star would weigh about a billion tons.
A neutron star the mass of the sun would be about the size of Chicago. A neutron star does not contract further because there is a repulsive force between neutrons that prevents this. The first confirmed neutron star was found at the center of the crab nebula which is a remnant of a supernova that was observed and recorded by the Chinese in 1004. It is known as M1. It turns out that the final collapse of a star also produces a spectacular explosion.
But stars above about 3.6 solar masses have a still different fate -- to become black holes. Above this mass there is no known force that can resist the gravitational force that results. The result is that in an instant the star collapses to a point. Probably not a mathematical point since there is a small scale distance limit. Quantum mechanics places this limit of smallness at 10-33 meters. At lengths shorter than this space and time are thought to become confused.
But if a star could collapse to a mathematical point its density would become infinite. So would the gravity at its "surface". It might even make sense to say that it continues to collapse forever. At this stage the star becomes a "singularity". Within its boundaries the laws of physics no longer apply. As a matter of fact the star ceases to be a part of the universe in any sense.
But this is not yet the black hole.
More Gravity
I said before that gravity is the weakest of the 4 forces. So you may be surprised that it is able to do what I describe. The key is the mass density of the objects we are discussing -- the amount of matter in a given volume -- and the distance from the mass. At the surface of the earth this density is "normal". You and I have no significant gravitational attraction though the earth is massive enough to hold us and the air we need to breath.If you were to go up in a plane with a scale and weight yourself you would find you are lighter than you are here on the ground. The reason is you are farther away from the attracting mass of the earth. The further way you are the less you weigh. Your mass and the mass of the earth have not changed. What changes is the gravitational force (falling off with the square of the distance). Technically the mass density of the space below the plane has fallen because it includes some air as well as the earth and the air is much less dense than the earth.
If you could go down into the earth (say in a tunnel or cave) what would happen? The surprising answer is that you would get lighter. It is surprising because when you came down from the plane you got heavier and you'd think that if you kept on going you'd get heavier still. The reason you don't is that as you do down into the earth there is some part of the mass of the earth above you pulling you up. If you could get to the center of the earth you'd be weightless! The entire gravitating mass of the earth would be all around you pulling you in all directions and all these pulls would cancel out.
To get the expected result you must shrink all the mass of the earth so that it is always below you as you descend. If you were to do that you would also increase its mass density. You could just as well shrink it down to a point located at its center with infinite mass density. If you do that the gravity at the surface (or where the surface was) would still be the same. But as you descend below that you get heavier and heavier.
Another feature of gravity at the surface of the earth is that if you throw a stone into the air it falls back down. If you want to throw the same stone higher you have to throw it harder (which actually causes it to leave your hand faster). If you wanted to throw the stone so that it never returned you'd have to throw it about 25,000 mph. This speed is called the escape velocity at the surface of the earth and is a function of the gravitational field.
At higher altitudes the escape velocity goes down just like your weight and for the same reason. Correspondingly if you descend into the gravitational field of our shrunken earth of the imagination you find that the escape velocity increases. In theory it can increase to 300,000 kph (186,000 mph) which is the Speed of Light and beyond. I say in theory because the mass of the earth is so small that the point where this will happen is corresponding small and cannot be easily reached.
The Black Hole
So lets go back to talking about stars and especially the massive kind that become singularities because in their case about a mile or 2 from the singularity the gravitational pull will be so strong that the escape velocity will rise to the Speed of Light. Any light emitted from this point in space will not escape from the vicinity of the singularity but will instead curve back and fall into it!I should probably note that Einstein's contribution to all this was to show that light behaves like a particle in the presence of gravity. Light rays that pass through a gravitational field are deflected toward the gravitating body just like a bullet being deflected toward the ground. At the surface of the earth the gravity is so weak and the speed of the light bullet so fast that this is hardly noticeable. Near a star like the sun the effect is measurable. Near a singularity it is dominant. The result is a black hole -- a sphere from which no light can escape.
Note that this is not a solid surface but a distance from the singularity dependent only on the mass of the singularity. You could fall into it. But because nothing can travel faster than light, you could never escape having once done so. If fact once inside this sphere which is called the "event horizon" you would quickly be sucked into the singularity. And you would be shredded by the near infinite gravitational potential in the process. In short you'd die. We think.
Gravitational potential here refers to the fact that close to a massive body having a correspondingly strong gravitational field any part of your body closer to the massive body is pulled harder than other parts further away. You would really be pulled apart! I have to say "we think" because we could never observe your death or anything else that happens within the event horizon. No information can escape across that boundary.
About twice the diameter of the event horizon there is another interesting phenomenon called the "photon sphere". (A photon is a particle of light.) At this distance an object traveling the speed of light is able to orbit the black hole. Therefore light itself is able to orbit the black hole at this distance!
Black holes are said to be the Cheshire Cats of the universe. They are stars that have disappeared leaving behind only their gravity -- like the Cheshire Cat's smile in Alice in Wonderland. The only physical fact that can be known about whatever is in a black hole is its mass. As noted above we can never observe anything that happens within the event horizon. Stars that collapse into black holes therefore don't have to reach a singular state to disappear from the universe. They essentially do that when they have shrunk to within their own event horizon.
Stellar black holes are not the only kind of black holes. Some theories suggest that mini- black holes with the mass of a few million kilograms were born in the Big Bang at the beginning of the universe. Some theories suggest that the cores of galaxies harbor massive black holes with a million solar masses and more. These would have to be formed either in the Big Bang or by millions of stars falling into a normally formed black hole.
Seeing Black Holes
The only way a black hole can be detected is through its interaction with other objects. Things to look for are objects that are in very small orbits moving at high speeds or objects that are highly luminous at high energy (x-rays and gamma-rays). The two features might go together. Black holes in binary stars might be detectable.What might happen in such a case is one of the stars in a binary system is probably going to be more massive than the other and therefore run through its nuclear fuel faster (the more massive a star the faster it will consume its fuel and also the more likely is it to become a black hole). Once the black hole is formed in orbit around the remaining star it can pull gas off that star. The gas will not fall directly into the black hole but will be pulled into orbit around it. This orbiting gas will form a disk structure called an accretion disk. Gas in the accretion disk will be heated to star core temperatures by friction and compression. But there will be no outer layers of overlaying gas to hide this hot gas from our direct view as there is in a star. It will radiate intensely at high energy.
A great deal of evidence has been seen for the signature of a black hole in some binary x-ray stars. Some studies with the Hubble Space telescope suggest evidence for massive black holes at the centers of some galaxies. In science every result is always tentative -- subject to revision later as better methods and observations become available. But we seem to be on the way to confirming theory at least for stellar black holes.
One of the things people get confused about is they think a black hole is a giant vacuum cleaner sucking up everything around it. This typically leads to the question, "What would happen if the Sun became a black hole?" Answer: It would get a lot colder and darker because there would be no more sunshine, but nothing else. The earth would not get sucked into the black hole sun. It would just continue to orbit around it. It would continue to orbit around the sun whether the sun puffed up into a giant or shrunk down into a black hole because the gravitational attraction of any mass is the same as if all the mass were concentrated in a point at its center. And as long as you are not inside the puffed up sun or the event horizon of a black hole things are pretty much normal, status quo, no change.
I did mention above that in a binary system gas can get sucked off one member to accrete around a black hole partner. Actually that is misleading. What really happens is that when a star becomes a red giant as it ages the outer layers of gas are only loosely bound to the star because they are so far away from the center of mass. Since they are very hot they tend to "boil" off into space. This is in fact the process that forms planetary nebula. Most of this gas will be attracted to any companion because after all they are gravitationally bound (they orbit each other).
Another subtlety is that this gas cannot fall straight into the companion. The reason is that it is probably moving in another direction other than directly toward the companion. As the companion pulls this gas in this other motion is increased the same way a spinning figure skater spins faster when they pull their arms toward them. This phenomenon is called conservation of angular momentum. The result is that the gas ends up in orbit around the companion as soon as it reaches orbital speed at whatever distance it is. It can't then fall into the companion until something else happens. Like friction. This guarantees that these processes can last a long time.
Friction heats the gas, which also forms a disk because, well, anything that is not in the disk has to pass through the disk twice in every orbit around the companion. Eventually the disk just sweeps up all the material that is not in it. As the gas heats, it radiates energy. The energy has to come from somewhere so the gas loses orbital energy and spirals closer to the companion. Eventually it will spiral to within the photon sphere and quickly spiral into the event horizon and then be sucked directly into the singularity.
Into a Black Hole
At the photon sphere the view is spectacular. If you look away from the black hole the sky appears normal and star studded. If you look into the event horizon you see nothing. If you look perpendicular to these two opposing directions you see a perfectly flat "horizon" separating the black below from the sky above. You see that the sky near the horizon contains more stars than it should, crowded closely together. This is because the light you are seeing has been bent almost completely around the black hole. The stars you are seeing near the horizon are actually on the other side of the black hole below you! If there is an accretion disk around the black hole you are orbiting you will be able to see all of it though it is likely to be highly distorted.At the event horizon things start to get weird. Above I said that the event horizon is that place in space around the singularity where the escape velocity reaches the speed of light and light cannot escape. That's a simplification. It sounds like light stops doesn't it? But light can't stop. As a matter of fact Einstein said that light will always have a speed of, well, the Speed of Light. This will also be true of light emitted from near an event horizon. If you are some distance away and you measure the Speed of Light emitted from a point near an event horizon you will find that it is traveling 300,000 kph rather than 300,000 kph - the escape velocity at that point.
So what does happen that we cannot see light from beyond the event horizon? First think about what happens to a rock when you throw it up in the air on earth. It falls back. Why? What happens? When you throw the rock you give it some energy -- kinetic energy, energy of motion. When it stops moving at the height of its flight it has lost all of that kinetic energy. (Technically all the kinetic energy has been converted into potential energy which in the ensuing fall again becomes kinetic energy, but we will ignore that.) Now think of a particle of light in the same situation traveling straight up. It too has energy and the only way it could fail to continue to travel away from an event horizon (or any other gravitational source) would be to lose energy.
Now light particles are quantum objects and as such they have both particle and wave properties. And the wave length of light is proportional to its energy. Long waves like infra-red are low energy. Short waves like ultraviolet are high energy. In a gravitational field light loses energy just like the rock. But instead of slowing down and stopping like the rock which it cannot do it just changes wave length. The light emitted from near the event horizon is severely reddened and at the event horizon appears to an external observer to have an infinite wave length. As an object falls into the event horizon it appears to an external observer to become redder and redder until its light is completely shifted into long wavelengths that we cannot see and then ceases to "wave" altogether.
What does another observer who rides this object into the event horizon see? Visually the "horizon" seen at the photon sphere quickly rises up and closes at a point straight over head. Does she see the light being emitted by the particle become redshifted? No she does not! The reason is that relative to her (she is falling with the particle) there is no change in energy at all. This is one of the surprising consequences of GR that what two people see will be different according to their "frame of reference". Specifically frames of reference in motion relative to each other see the same event differently.
Because the frequency of light is a time dependent phenomenon (it's measured in cycles per second) the fact that an observer far from the black hole and another observer descending into the black hole see the frequency of light emitted from a particle near the event horizon differently tells us something about time near the black hole. For the distant observer time appears to slow down on the particle that approaches and to stop at the event horizon! The observer on the particle sees something quite different.
Her time appears not to change at all. But because light falling into the black hole picks up energy and therefore its wave length becomes shorter it appears as though time speeds up for objects far from the black hole that emit this light. This includes the whole rest of the universe! The observer riding the particle into the event horizon sees the universe speed up and eventually all of future history passes in a flash when she reaches the event horizon.
Remember, these relative time effects are the result of gravity alone. They also happen in normal space like at the surface of the earth but the effect is just so small that it doesn't really make a difference. In the strong gravity near a black hole these effects become easily visible. Also, they are clues that GR treats space and time as the same thing -- just different dimensions in a combined spacetime. Near a black hole spacetime (not just space) is being radically warped and the interchangability of space-like and time-like dimensions becomes real.
There are more predicted effects that we could discuss, but I think that will be left to a future iteration of this page. You should realize that this has been a descriptive treatment of black holes. All of this has a mathematical description which I do not even presume to understand but which you may wish to pursue. Anyhow this is enough information to make you really dangerous as they say and evoke all kinds of questions that you can check out on your own and see if I got it right.
Welcome to the universe of black holes.
Back to the Top | What is a Black Hole? | Gravity | The Life of a Star | The Death of a Star | More Gravity | The Black Hole | Seeing Black Holes | Into a Black Hole
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Created December 3, 2001,