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

Crossection of a static black hole

Why is it called a static black hole?

It has no charge and it is not rotating. This is your standard, idealistic, simple black hole. It is also called a Schwarzschild (Swar - shild, not Swarts - child) black hole. The interesting places for this one are the photon sphere, the event horizon, and the singularity. What happens to you near the black hole all depends on your distance in Schwarzschild radii. Let us say that you're flying towards a static black hole in a brand new, top o' the line spaceship. You're approaching the black hole slowly, since only a fool would charge full-speed into one.

The black hole itself is very plain and quite difficult to actually see, presuming that you are looking at a black hole with absolutely no accretion disk. It's the space around it that is interesting. You see multiple images of many of the stars. That galaxy that you know is behind the black hole appears as a ring around the black hole, commonly called an Einstein ring. Why you see the galaxy at all, when the black hole is between you and it, and why it appears as a ring is from the bending of light due to the strong force of gravity of the black hole. Say you have an iron marble and a bar magnet. If you roll the ball near enough the magnet, it veers towards the magnet. The marble ends up tracing a slightly bent path versus the straight path it would have traced had it not encountered the magnet. Now replace the magnet with the black hole, and the marble with a light ray, and you've got it. The light from the 'hidden' galaxy peeks around the black hole and looks like a ring. Cool neh?

As the ship passes closer, there's a sudden flash to the rear. Backing up and hovering, you discover that ... it's the back of your own ship? Oh, this is the photon sphere.

The Photon Sphere

Mathematically speaking, the photon sphere occurs at 3/2 the Schwarzschild Radius. It's the only place where light rays can have (very) unstable orbits around the black hole. Why is it called photon sphere? Photons orbit there ... and it's a sphere. You know how it takes a certain speed to stay at a certain orbit? Satellites closer to the earth must move faster than satellites farther from the earth or else they will fall onto the planet below. It's the same way with a black hole, just the numbers are larger and the results more dramatic. As you approach the black hole, you can orbit all you like. It's just that the closer you get to it, the faster you've got to go to stay in orbit and not fly off into space or plummet into the black hole.

At the photon sphere the speed you would have to go to stay in orbit is c, the speed of light, some 3 x 108 meters per second. Say you hovered your ship in an orbit just above the photon sphere (which would take tremendous energy, for you'd be going a significant fraction of the speed of light) and stuck a camera down into the photon sphere (just suppose...hypothesize). The back of the camera sends off light rays that hold temporary orbits around the black hole. A light ray can bounce off the back of the camera, orbit around the black hole, and run smack into the front of the camera. If you try to move the camera towards the image, the image recedes. Why? Well, think about it. The view the camera has is like the view someone would have if they are standing behind it. If the camera stands behind someone and they start to move forward, well, their image recedes.

I keep saying these light orbits are only temporary, but why is that? Why can't a light ray stay in the photon sphere forever? Firstly, the photon sphere is a tiny place --- just one precise distance! A light ray would have just one chance to hit the right trajectory. Secondly, things aren't that precise out there in the universe. There are all these other light rays bouncing around, making things very unstable. A light ray may orbit the photon sphere for a long time, but, eventually, it will encounter another light ray and its perfect orbit will be disturbed. It might go flying off into space only delayed a thousand years, or it could fall into the black hole. You want to argue quantum mechanics and say there is always the possibility that it would orbit forever? Fine, but that's one possibility out of too many to count!

Okaaaay, the photon sphere is fun, but it loses its charm after a while. You take the rocket closer to the black hole. It is now impossible to orbit the black hole, but it is still possible to stay at a constant radius --- to hover above the black hole. Now, you approach the ... event horizon (the astrophysical thing, not the movie). The what??

The Event Horizon

When people talk about the black hole, they're usually referring to its event horizon. The funny thing about the even horizon is that it, just like the photon sphere, is just a mathematical construct, a distance. If you wanted to get theoretical, it is the first sphere of light (which is, of course, constantly expanding at the speed of light) that does not expand (due to the extreme curvature of spacetime). Enough, enough, what is it?! Rs, the Schwarzschild radius. What makes it special? Once something passes beyond the event horizon, it can never leave the black hole and is doomed to a painful stretchy demise.

Ah ha, that's interesting.

Your rocket ship can come close to the event horizon and (by firing all the rockets at their strongest and wasting a lot of fuel and, not incidentally, squishing you flat with the acceleration) can move away from it. This all has to do with something called escape velocity. You know how, when rockets are launched on the earth, they have to go a certain speed or else they'll just plummet back to the earth? That's escape velocity: the speed needed to leave a gravitational field. Want a peek at the equation for escape velocity? Black holes have escape velocities just like anything else, it's just that the numbers are orders of magnitude bigger than the escape velocities of planets. The closer to the black hole's event horizon, the greater the escape velocity. At the event horizon the escape velocity is the speed of light. Things with mass can't go the speed of light, so, if they get to or go closer than Rs, they cannot escape the black hole. Beyond the event horizon the escape velocity is greater than the speed of light. Light rays that go beyond Rs can't even get out!

Why is it called the event horizon?

Well, we who-are-further-away-than-Rs can't see the light rays emitted by something at Rs. Say we had thrown something into the black hole. We could see its image get smaller and smaller as it approached the black hole. Then it would start to move slower and slower and get dimmer and dimmer. The slowing down and the dimming are the effects of the strong gravitational field. The thing we threw would slow down until it seemed as if time had stopped for it, and it would dim until we needed an infrared detector to see it. The last image we could see would be the light emitted just before it crossed the event horizon. It's the last event we could see. Get it?

BTW, if you stuck your hand past the event horizon of a black hole, you could pull your arm away (not really; your muscles and bones would snap from the strain, but let's just be hypothetical for a minute), but the part of your hand that went past the horizon would forever remain there.

While moving towards the event horizon, you look out your front and back windows (high-tech spaceships have lots of windows --- neat!) because you're curious about the effects of the gravitational field on light (or you're just really bored). The view from the front window is boring, for all you can see is a large black area getting much bigger. The back window is much more interesting. From the back window you can see the view of where you came from is ... shrinking?

Why is this? Well, it has something to do with a thought-device normally used when considering the formation of a black hole. It's called a light cone. In short the cone describes the range of angles that are "escape paths" for light rays released from a collapsing star. As the star gets closer and closer to its Schwarzschild Radius, the light cone gets smaller and smaller. Eventually, it closes up completely, when the material collapses to its Rs and the event horizon forms. It's kinda the same thing when you move towards the event horizon and the angular size of your universe shrinks. It's the light cone closing up. Spacetime's way of reminding you that the chances of you getting away from the black hole are fewer and fewer the closer you get to the event horizon. At the event horizon the cone closes and the view of your universe condenses into a single point.

Now, I'd like to clear something up. This whole business of hovering around a black hole's photon sphere or near the event horizon is quite speculative for one major reason: acceleration. I rather blithely spoke of hovering at the photon sphere --- if real humans were to try that, they'd be squished by the acceleration of their rockets! We're not talking a couple G's of force --- for the smallest possible black hole for a 100 kg person that force would be 2.9 x 1015 Newtons!! (By comparison, the force of gravity on a 100 kg person from the earth is 1,000 Newtons.) People just can't survive that kind of acceleration. Most things can't. Still, it's rather useful to say such things in order to get a good feel for what happens around black holes.

Onward to inside the event horizon!

What happens when you cross the event horizon?

At first....well, nothing noticeable unless you consider the closure of the light cone to be significant. Had you been looking out the back window, as previously mentioned, you would have seen the view of your universe shrink to a dot and disappear; but there is no Star Trek force field effect to tell you when you cross. What you see and feel next all depends on your reaction to the fact that you are now doomed to a painful stretchy death. You could fire your rockets full blast in the hopes of surviving a little longer by braking, or you could shut off the engines to make your last few moments as comfortable as possible. It's a choose-your-own-adventure black hole!

Beyond and to the Singularity!

I keep saying that, when you pass the event horizon, you keep falling...but towards what? Outside of the black hole, you always fell towards the event horizon. What's inside? The answer is a little tricky. You'd best check out the Inside section singularities, if you want the exact answer. Obviously, the singularity is at the "center" of the black hole, according to my own diagram at the top o' the page. It's that little green dot. Is there really a little green dot at the center of a black hole? No ... there's no real center and there's no little green dot. Okay, an interpretation of gravity is the bending of spacetime. Outside and close to the black hole spacetime is bent a lot, but the curvature is still finite. The closer you get to the singularity, the more spacetime is bent. At the singularity the curvature of spacetime is infinite, theoretically.

There's no center and there's nothing there except a lot of bent spacetime. This sure does make sense, Jillian. Sorry, but the singularity is a darn strange place (er, a strange time, that is). What happens near to it and what it is depends on quantum mechanics. Accept this: the singularity of a static black hole is described as a point at which spacetime is infinitely curved. I cannot give you a satisfactory physical interpretation of that sentence, since infinites are oogy to actually show.

 

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