3.7 Black Holes

Critical Questions:

  • What is a black hole?
  • What happens near a black hole?
  • How do we know they exist?
  • What about wormholes?

In order to explain what black holes are like, I’d like to relate to you the following parable.

A bunch of physicists are up late one night. They’ve been at a party. Most of the guests have left by now, nobody’s noticed that the music has stopped, and the air smells only faintly of sweat and a remarkable range of mind-altering substances. Somebody is passed out on the couch, but no one seems to know who it is. During a lull in the mumbled conversation, one of them happens to look up through a skylight and see the stars. She begins to think about how far that light has travelled to reach Earth, and about why it didn’t just stay where it is. She says so, out loud. One person mumbles in agreement. Another person suggests that maybe some stars don’t allow their light to leave at all. This sparks a two-hour long discussion that includes a whole complement of theories related to this kind of dark star, with names like the no-hair theorem and the information loss paradox. Before the last of them finally falls asleep, he mutters, “Black hole. We can call it a black hole.”

Chemistry Dog
Or maybe it was this guy.

To the best of my knowledge, this is not a true story. But if you learn enough about black holes, you might be tempted to think that this is how people thought up the idea.

We’ve already seen that light, being massless, is not affected by gravity in classical physics, whereas in General Relativity, the trajectory of a beam of light can change due to gravitational spacetime curvature. As people worked with Einstein’s equations, they soon discovered one very interesting possibility: in a strong enough gravitational field, nothing – not even light itself – would be able to escape. Space and time would be so tightly compressed that you would have to be travelling faster than the speed of light to ever get out of it.

This is a black hole. It is not really a hole at all, but it is black because it lets out no light. And it’s not really as mythical as it sounds: since gravity gets stronger with more mass and with less distance, all you need to do to create a black hole is get a big enough mass compressed into a small enough volume. If you can do this, then within some distance from the object (called the Schwarzschild radius), the gravitational field will be strong enough that nothing will ever escape from it.

In this basic sense, anything at all could be a black hole if it were squeezed into a sufficiently tight space. To turn the Earth into a black hole, for example, you’d have to squish it down to about the size of a peanut. But in practice, it takes quite a bit of energy to compress something enough to create black hole conditions. You need something as big as a star.

While a star is still burning1, the heat energy it emits keeps the star expanded to a certain size. But eventually, once all of its fuel runs out, there will be no energy left to counteract the attractive gravitational forces of all that mass, and the star will collapse. Depending on the size of the star, it may end up as something called a white dwarf or a neutron star. But if it’s at least three times as massive as our sun, it’ll collapse into a black hole.

black hole
In this simulated image of a black hole in front of the Large Magellanic Cloud, gravitational lensing causes a distortion resembling an actual hole.

Nothing can ever come out from within the Schwarzschild radius – no energy or matter of any kind.2 Black holes can swallow planets, stars, and anything else nearby. And if you’re outside of a black hole, you have no way to tell what’s inside. All you can determine is its mass, its electric charge, and how fast the whole thing is spinning. This is the so-called ‘no-hair’ theorem (seriously), and it results in the aforementioned information loss paradox: you can determine a lot of things about an object outside of a black hole, but once it falls in, all of that information becomes inaccessible. For similar reasons, the Schwarzschild radius is also called an ‘event horizon’,3 because nothing from inside of it can ever have a causal effect on anything outside.

The extreme curvature of time and space near the event horizon has some strange effects. For example, if you were near a black hole and watching an object fall towards the event horizon, you’d see the object slow down as it approached, rather than speed up. Weirder still, you would never actually see it cross the event horizon – from your point of view, it would essentially stop right before passing over that invisible line. But if you yourself were falling towards the event horizon, time would pass normally to you, and you’d keep accelerating down towards the center of the black hole.

(The professor who taught me relativity at university told us the following in his first lecture: when you’re doing most kinds of physics, you should always check to be sure that your answer makes sense. When you’re working with relativity, any answer that makes sense is probably wrong.)

Unfortunately, if you actually were falling into a black hole, you’d be too busy dying a horrible death to stop and look at your watch. Remember how the moon can cause tides because its gravitational force is stronger on one side of the Earth than on the other? Well, near a black hole, the tidal forces are enormous: the force of gravity gets significantly stronger with every inch as you approach. The difference is so great that if you’re falling feet-first, your legs will be pulled away from your torso, and your torso will be pulled away from your head. I don’t think I need to go into all that much detail, except to point out that this process actually has on official name: spaghettification. As in, you get turned into one long and late piece of spaghetti.

Spaghettification, By Theresa Knott [Wikipedia]
This gif by Theresa Knott proves that falling towards a black hole is a bad idea.
But most of these insane ideas only involve what happens close to or beyond the Schwarzschild radius. Beyond that distance, the gravitational effects of a black hole are no different than than those of a star of the same mass. For example, stars can have stable orbits around black holes in the same way that two stars can orbit each other. Astrophysicists are even confident that there is probably a “supermassive” black hole at the center of almost every galaxy, including one that’s four million times the mass of the sun in the middle of our own Milky Way. The gravitational pull of each of these black holes is crucial to holding all of those stars in their orbits around the galactic central point.

If you’ve been thinking carefully so far, you might have come up with yet another clever question: If black holes emit no light or information of any kind, how do we know if any of them actually exist out there rather than merely as theoretical possibilities? Well, we do have some pretty solid observational evidence for the existence of real black holes in outer space. For example, if we can see a star moving in a little circle with nothing in the center, there’s a good chance it’s orbiting a black hole. But even better than that, theory shows that things orbiting or falling into black holes emit very specific types of x-ray radiation, and we’ve already found a number of signals that match these patterns.

So black holes almost certainly do exist. But there’s another type of spacetime curvature which is a little more controversial: the wormhole. In order to get an understanding of a wormhole, you’ll need to go back to that analogy of space as a bedsheet. This time, instead of dropping something heavy onto it, grab two spots anywhere on it and pull them together. If those two spots could be joined somehow, you could traverse huge distances instantly – never exceeding the speed of light, by the way, just kind of stepping around it. (This is, again, a clumsy 3D analogy for what is really a 4- or 5-dimensional phenomenon, but you get the picture.) Worse yet, with a few relativistic tweaks, wormholes could actually be used to travel backwards through time.

Unfortunately, the mathematics imply that any kind of stable, traversable wormholes would require either negative energy, or particles with negative mass, or some other as-yet imaginary object.

Or we could just ask these guys how they did it.

As we end this chapter, it becomes even more obvious why an understanding of gravity has eluded us for so long, as we discussed in the introduction. It’s invisible, mysterious; at once immensely powerful and surprisingly weak; it plays by its own rules, and any attempt to make sense of it only seems to lead to more questions. But I suppose this could be said of almost any topic in physics, which is why I still have so much more to tell you about.

Big Ideas:

  • A black hole is simply a large amount of matter in a small space. If a star is big enough, it will collapse into a black hole when it runs out of fuel.
  • The gravitational pull is so strong around a black hole that within a certain distance (the event horizon or Schwarzschild radius), nothing at all can escape – not even light.
  • There is strong observational evidence for the existence of black holes in space. There is (probably) a black hole at the center of every galaxy.
  • A wormhole is the connection of two points in space due to spacetime curvature. Traversable wormholes are only possible according to certain theories and may not really exist.

Next: 4.1 – Introduction to Fluid Mechanics

Previous: 3.6 – General Relativity

  1. I.e., the atoms inside of it are still undergoing nuclear fusion reactions and emitting energy as heat and light.
  2. Technical note: in 1974, Stephen Hawking discovered that according to quantum mechanics, black holes should actually emit some radiation. The mechanism for this is way too complicated to get into in a footnote, but if it were true, then black holes could evaporate over time as they lose energy.
  3. Another technical note: only a non-rotating black hole has an event horizon at the Schwarzschild radius.

4 thoughts to “3.7 Black Holes”

    1. The Schwarzschild radius comes from a solution to Einstein’s field equations for black holes that (among other properties) are non-rotating. Rotating black holes distort the spacetime around them in a second way, which is often referred to as a kind of ‘dragging’ effect. So if you take angular momentum (rotation) into account, you get a different Event Horizon than you would if you just calculated the Schwarzschild radius.

  1. A completely random question: Assuming that black holes do exist, and that nothing can ever escape them, is there a way to simulate how black holes form, and to estimate what kinds of new elements are being fused within them? Can we estimate the properties of those elements without even knowing of their existence?

    1. That’s a great question, and I don’t know much about it! The amount of crazy relativistic physics going on inside a black hole requires some pretty advanced math. But probably the biggest problem with answering your question is that black holes are still an area of active research, and there’s a lot of disagreement about what exactly happens inside them.

      In fact, whole new fields of physics, like Quantum Gravity, have been developed (in part) to be able to tell us what happens to matter inside a black hole. You see, although General Relativity is an extremely successful theory, it doesn’t agree with Quantum Physics at the level of the very small. In other words, we can tell a lot about what must be happening near a black hole, but there are still a lot of unknowns about the inside of one!

      Anyway, when you’re dealing with the kind of immense pressures that come from such a strong gravitational field, particles stop organizing themselves into discrete atoms (i.e. elements) and tend to create strange new phase states, like plasmas and whatnot.

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