Gothos: Jillian's Guide to Black Holes

Jillian's Guide to Black Holes: Forming - Types - Outside - Inside - Finding - References - Websites

Black Holes by Supernova

Firstly, a black hole isn't really a hole at all, but that's the easiest way to think of its effects on the rest of the universe. Take a star that's at least thirty times larger than our sun and make it explode (called a supernova). Stars do that at the end of their lifetime, sometimes leaving a remnant of the violent explosion. The nature of the remnant depends on its mass. If the remnant is less than 1.4 solar masses, it will become a white dwarf, a kind of hot dead star that isn't bright enough to visibly shine. If the remnant is roughly 1.4 solar masses, it will collapse. The protons and electrons will be squished together, and their elementary quarky particles will recombine to form neutrons. What you would get is small (by stellar terms) sphere of neutrons with perhaps a thin film of electrons and other stuff at its surface. That's why it's called a neutron star. See, the neutrons don't mind hanging around near each other; but if you get them close enough to each other, they get anxious and resist being pushed any closer. (Yes, I'm attributing emotions to sub-atomic particles.) The neutrons of a neutron star are, indeed, pressed quite close to one another and exert a certain pressure on each other. This pressure prevents the further collapse of the neutrons star. If the remnant is larger than 3 solar masses, it becomes a black hole (well, 2 or 3 depending on who's giving you the number). I think that calculates out to a star roughly 30 solar masses before supernova.

Superstar Eta Carinæ²

For example, let's pick Eta Carinæ, a superstar that is hundreds of times larger than the sun (also 8,000 ly away) and happened to have exploded around 1850ad.² That and I have a nice current picture of it. Very well, Eta Carinæ goes supernova! In a supernova the atmosphere of a star collapses onto and compresses its core, and the remaining mix of stuff is blown into space leaving a remnant of the core. During the earlier part of the star's life, it fused hydrogen into helium. During the later part of its life, it fused helium into the heavier elements, which made their way to the core of the star. In the last split second of its life, as waves of energy push out from the collapsing core, the star fuses its atmosphere of helium (and a few other things) with its core of iron. This is called nucleosynthesis. This process created ALL the atoms heavier than iron or nickel. These heavier atoms plus millions of neutrinos are thrown out in waves as the star collapses, leaving the remnant.

Now, since Eta Carinæ's remnant is larger than three solar masses, the pressure of collapse and the force of gravity of all that mass squishing the core (which is very hot metal) condenses all the matter together. No more electron shells and orbits --- the neutrons are forced together. Then, the very neutrons themselves give up and get squished by the pressure. The pressure of the neutrons not wanting to be too close together is what balanced the force of gravity of all those neutrons. Since the remnant is heavier than 3 solar masses (or two solar masses ... the calculations are sensitive to slight changes, so depending on how one sets up a model, one gets different answers for the mass). The force of gravity is stronger than the pressure of the neutrons. At this point the remnant cannot support itself from its own gravity, and it collapses. Actually, the formal way of saying this is that there's a radius that determines whether the star can squish itself into a black hole. It's called the Schwarzschild Radius (swar - shild). If the starstuff can collapse itself smaller than R_s (the Radius), stand up and cheer, for it has become a black hole. There have been proposals of steps between the neutron star and the black hole, such as a remnant composed of quarks, but I don't know anything beyond that.

What does it look like as the star collapses?

If you were to watch Eta Carinæ becoming a black hole, you would first see the dramatic and wonderful supernova, in which the superstar forcefully ejects most of its atmosphere very quickly. It's a violent process but quite pretty. After enjoying this for a while, you would see the star itself start to collapse. After watching this for a while, you would think it mighty peculiar that the star seems to be slowing down and getting redder and dimmer as it collapses. What's all this?! These are the effects of the gravitational field getting stronger. Okay, a brief side-note about gravity and light cones.

Light cones

In the presence of a gravitational field time slows down. You don't sit there and wonder why your watch is running slower. Everything slows down --- your watch, your brain, your cells, your very atoms --- everything. Someone who is outside the field would watch you and wonder why you're moving so slowly (and you would wonder why they're moving so quickly). This effect is called time dilation.

You've probably heard many times how the speed of light is a constant in a vacuum. Suppose you have a light ray in a gravitational field (hey, happens every day!). It can't slow down like your watch and your brain and your cells and your atoms because it's light in a vacuum and it must go a constant speed. So, does it just keep going regardless of gravity? No way! The speed of the light ray can't decrease, but the frequency can. Oh, tricked you with that frequency bit, hunh? Light is formally known as electromagnetic radiation (I shall only type that once, here, for it is a long word and I'm liable to mis-spell it). What that means is that light is really a changing electric field (which induces a changing magnetic field, which induces a changing electric field, blah, blah).

The important part is that light can be thought of as a wave in some respects, just like a wave in the ocean. Just like water waves, light rays have a frequency of arrival and a wavelength (one being the reciprocal of the other). The longer the wavelength is, the fewer waves can come in during a certain time, thus the lower the frequency. Got it? If a yellow light ray passes through a very strong gravitational field, its frequency will lower and it will appear reddish. Fine, fine, fine. That explains the color shift, but what about the slowing down bit? A very useful concept for explaining this is the light cone. Imagine that all the possible paths for light to take can be summed up in this cone shape. Why? Uhhh ... it comes from a three dimensional interpretation of the two light rays from a spacetime diagram. Just ... go with it. If you were on a planet, that cone would describe what directions the light would have to shine in order to escape from the planet's gravitational field. Normally, light can escape from planets and stars. They shine, y'see!

However, it all depends on the strength of gravity. Imagine the light rays being emitted from poor ol' doomed Eta Carinæ. As the star collapses and approaches its R_s, the gravitational field gets stronger because there is more matter in a smaller place. Certain light rays (such as those shot out in a tangent to the star) will fall back down on the star because the gravity is so strong. The light cone becomes narrower. When the star is very close to R_s, the light cone is quite narrow, and only those light rays that travel out almost perpendicular to the star's surface will escape the gravitational field. When Eta Carinæ reaches R_s, the light cone closes, the event horizon forms, and light can no longer escape.

Back to what Eta Carinæ looks like as it collapses.

The star will continue shrinking, but as it neared R_s it will be so dim that you would probably need an infrared detector to see it. Really close to R_s for all intents and purposes Eta Carinæ has become a black hole. I've heard different sources give different times for this process. Some say it takes forever for the last photon to escape. Some say that it will take a quite a short time. It's all quite iffy, since we've never actually seen it happen. True that there might still be photons coming at you that escaped before the event horizon formed and are taking their sweet time about getting away.

Does the black hole just stay that size forever?

No way! The black hole has a certain mass and size of its event horizon when it forms, but that changes over time. If stuff falls into the black hole like dust and light, its mass increases. If its mass increases, its R_s gets a little larger. Therefore, if stuff falls in, the event horizon gets a bigger. The idea that black holes could only get larger feels weird to me, so I'm quite happy to say that there is also a reverse process, where the black hole gets smaller. It has to do with Hawking radiation. In short it is possible for particles to form by stealing energy from the black hole. If the black hole loses energy (and energy = (mass)c²!), it gets smaller. Black holes are rather dynamic in that sense; you can always add charge to them, take charge away, make them rotate slower, and change their size.

Should the sun become a black hole, the earth would not immediately plunge toward it.

BTW, if the sun were to suddenly pop into a black hole (no, it can't actually ever be a black hole, but just imagine), would the earth go plummeting into it? No, it would continue on its orbit and things would get rather chilly, that's all. The black hole exerts the same gravitational force on stuff around it as a star with the same mass would. Things just get interesting close to the black hole.

Don't believe me? How about this argument. When calculating forces of gravity from objects on other objects, we talk about the distance between the two of them. Does this mean the distance from the surface of the one object to the surface of the other? No. We talk about the distance between the two centers of mass, and, when considering stars and planets, that center is just the center of a sphere. Why? Well, consider yourself sitting in your chair. Right now, every darned atom in the whole earth is attracted to you (and you to each of them by Newton's Third Law, action and reaction). Now, each bit of the earth attracts you with a certain force and has a corresponding bit on your other side that attracts you with an equal force. Well, the force is actually to the side and slightly down, since you're standing on a curved surface. The side-to-side force cancels out and all you feel is the downward force, the force that points directly at the center of the earth.

And what does this have to do with the sun-turned-black-hole not yanking the earth out of orbit? I've proven to you that you can treat the force of gravity as just a force from the center of an object. The center of an object is just a point. As far as the force of gravity is concerned, it only "sees" mass and distance. Right now, for the case of you sitting on your chair, our calculation of the force of gravity does not care if the object doing the attraction to you has its mass spread out the size of the earth or whether it is concentrated in a theoretical point. We only need your mass, the mass of the earth, and the distance that separates you two. There are other considerations such as tidal forces which depend on how spread out the matter is, and then it would, indeed, be quite important that the mass of the earth fill the area of the earth, otherwise you'd be in a bit of an uncomfortable spot, sitting in that chair! Still, tidal forces are a topic saved for the the section on the effects outside of a black hole.

That was lengthy! My apologies.

Black Holes by Coincidence

A black hole forming without a tell-tale and quite noticeable supernova to warn the neighbors --- quite a frightening concept, isn't it? It is true, though. The definition of a black hole is just an object that has no matter when you check up to its R_s. Compress something to its Schwarzschild Radius and an event horizon forms around it. Oh, you don't believe me? There have been plans for creating particle super colliders which would endow a particle with enough energy to exceed its Schwarzschild Radius. How can this be? Where's the mass? Recall Einstein's famous correlation between mass and energy, E=mc². It takes a lot more energy to get the equivalent mass, but a powerful, next generation super collider could provide that energy. In fact, the little black holes generated would be very much like primordial black holes. What are those?

Primordial Black Holes

Only modern black holes need to have remnant mass greater than three solar masses to form. Way back when, according to astrophysicists of good repute, the universe was much hotter and denser than it is now. Due to this incredible density and energy, it wouldn't take much to kick together 3 solar masses' worth of energy/matter within a Schwarzschild Radius. Since these primordial black holes were so small, though, most of them would have evaporated by now. Those primordial black holes large enough to survive up until now would have the mass of an asteroid (10¹² kilograms), the size of an atom, and would emit gamma rays (highest on our scale of frequencies of light)¹. When the universe was 1/10,000 of a second old, those primordial black holes had a chance to absorb enough matter to have this mass. I recall one author saying that these little guys would be the best power source we could find. They are too small for us to worry about falling in, and they would put out lots of clean energy.

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