Black hole questions

 Who knew that, a dozen years after I wrote something trying to explain a bit about black holes, people would still be reading it?  I get questions from time to time from readers, and I’m happy to try to answer them.  As long as I’m writing answers anyway, I’ll go ahead and post them here in case anyone else is interested.

This batch is from a high school student named Brandon Thrush.

 1. I have a good idea of what the event horizon is, but I do not know what you mean when you say that it is actually moving outward at the speed of light; does this mean that the whole entire black hole is moving at the
speed of light?

This is a very subtle and potentially confusing idea.

Suppose that you dropped a flashlight into the black hole, and at the exact moment it crossed the horizon, it emitted a photon (that is, a little burst of light) in a direction straight out, away from the black hole.  That photon would be stuck on the horizon, never falling into the black hole but never getting further away either.  Now, one of the main ideas of relativity is that light always travels at the same speed (the speed of light, naturally!) no matter how it’s measured or by whom.  So that photon is, by definition, traveling at the speed of light, and yet
it’s staying right on the horizon.  The logical conclusion is that the horizon is moving at the speed of light.

You might say that this is just a silly word game: Why do I say the horizon is moving outwards, rather than saying that the photon is sitting still?  The answer is just that the idea that the speed of light is always
the same (which means that photons never sit still) is so powerful and useful that physicists hate to give it up.  We’d rather say that the horizon is moving at the speed of light — even though it never gets anywhere!  — than give up on that idea.

At this point, it’s customary to mention the quote from Lewis Carroll’s Through the Looking Glass, in which the Red Queen says something like “Here it takes all the running you can do just to stay in the same place.
If you want to get anywhere, you’ll have to go a great deal faster than that!”

2. When you give examples of two black holes, one smaller than the other, you say that in the smaller black hole you would be torn apart before you even reach the horizon, but in the larger one, you would not be torn apart until after you reach the horizon.  How can this be?

The reason is that the thing that tears you up is the “tidal force,” which has to do with the difference in the strength of the gravitational pull between one end of you and the other end.  If every atom in your body is
being pulled on (and hence accelerated) by gravity in the same way, you won’t feel any ill effects, but if one part of you is being pulled more strongly than the other, you will.  For a large black hole, the scale of everything is so big that there’s no real difference between the pull on your head and the pull on your feet: both are huge, but they’re essentially the same.  For a smaller black hole, each of those pulls is smaller, but they’re different, and that’s what matters.

3. When a black hole is formed, it is because of a dying star, but does the star suddenly collapse under its own gravitational force and what is left is its gravitational force field, called the black hole, or does the star gradually collapse into its own force field?

I think I like the first way of saying it better. Certainly “suddenly” is better than “gradually”: although the leadup to the final collapse is gradual, once the final collapse gets started, it’s very quick.

There’s another obligatory literary reference here, by the way: “Gradually and then suddenly” is the way Hemingway describes going bankrupt in The Sun Also Rises.
The big idea is that, before it collapses, a star exists in an equilibrium, in which the pressure caused by the star’s particles (nuclei and electrons) balances the pull of gravity.  When a black hole forms, the reason is that that balance couldn’t be sustained, and gravity won.  The particles get pulled in closer and closer to the center.  After that process is complete, all that an outside observer can detect is the gravitational field (which we often prefer to call the “curvature of spacetime.”)

4. When the star is collapsing into the center, what happens to the particles while reaching the center?  What is their fate?

Once they get very near the center, we have to admit that we just don’t know.  Everything we say about what happens to particles inside the horizon of a black hole is based on theory, not observation, since we never see the interior.  But at first (that is, immediately after crossing the horizon) we can have pretty high confidence in our descriptions of the process: the physical conditions at first are very similar to situations we see in other places, so we think we understand them.  But near the center, the densities and temperatures get very high, eventually passing out of the range where we think we understand the physics.

So here’s what we can say: during the collapse, the particles that are falling in towards the center get compressed to higher and higher densities and higher and higher temperatures until, at some point, …. we don’t really know.

5. When a large black hole, such as a stellar-mass black hole, constantly grows, does the gravitational field extend farther and farther?  If so, would not the black hole eventually consume everything in the universe?

The first rule to remember is that a black hole of a certain mass has just the same gravitational pull as any other object of that mass.  So, for instance, a black hole the mass of the Sun attracts outside objects just as much as the Sun does, and no more.

Now, it’s true that as a black hole sucks in more stuff, its mass grows, and so does its gravitational pull.  But after the black hole has gotten all of the stuff near to it, it stops adding new matter at any significant rate, and so it stays pretty much the same after that.

In principle, every black hole in the universe is slowly adding more mass and hence pulling more strongly, but it’s important to emphasize the word “slowly.”  A typical black hole, after it’s had some time to clean out its immediate surroundings, grows at such a slow rate that even over the lifetime of the Universe we wouldn’t expect its mass to grow very much.

6. You refer to a large black hole as a “stellar-mass” black hole, but what are the different names given to the different sizes of black holes?  What are they from the smallest to the largest?

I have to admit that I’m not up-to-date on the subject of classification of black holes.  The last time I paid much attention to the subject, two main categories of black holes were thought to exist:

  1. Black holes that formed from the collapse of stars.  These typically have masses of about 10 times the mass of the Sun (plus or minus quite a bit).
  2. Black holes at the centers of galaxies.  A typical mass for these is  a million times the mass of the Sun.  The conventional wisdom seems to be that most large galaxies have one of these, and that they formed along with the galaxy itself.

When I talk about stellar-mass black holes, I mean the first category.  The other kind are most often called supermassive black holes.

It’s perfectly possible for black holes to exist with other masses. People have talked seriously about the possibility of microscopic black holes, for instance. But the black hole candidates that people have found in the
sky mostly fall into those two categories.  (I think that some black hole candidates have been found with masses in between the two categories — say around a thousand times the mass of the Sun — but I don’t know much
about that.)

If the Sun turned into a black hole

Some time back in the’90’s I wrote a document explaining some things about black holes.  To my amazement, people still read it, and they occasionally send me questions as a result.  I’m happy to answer these when I can, and as long as I’m answering them anyway, I might as well post them here.

The latest is from Chris Warring:

My friend and I are having a debate over the question “If the Sun turned into a black hole, what would happen to the Earth’s orbit?”

I quoted from your article  “What if the Sun *did* become a black hole for some reason? The Earth and the other planets would not get sucked into the black hole; they would keep on orbiting in exactly the same paths they follow right now….a black hole’s gravity is no stronger than that of any other object of the same mass.”

My friend argued that since astroids impact the Sun then they would also impact the black hole.  This would eventually increase the mass, increase the gravitational pull on the Earth, and place the Earth on a decaying orbit.

I have since read a little on Hawking Radiation, and that black holes evaporate.  I now wonder if the black hole that was our Sun would evaporate, losing gravitational effects on the Earth, and the Earth would end up drifting away from where our Sun use to be.

Here’s my answer:

First, let me say that all of the effects you mention are very small. They would alter the Earth’s orbit a little bit over very long times. When I wrote what I did about the Earth’s orbit, I wasn’t considering such tiny effects. But they’re fun to think about, so here goes.

It is true that, if the mass of the Sun (or black hole, whichever is at the center of the Solar System) goes up, then the Earth’s orbit will be affected. Specifically, it would move to a smaller orbit. And of course the reverse is true if the mass goes down.

First, let’s talk about what’s happening right now, and then consider what happens if the Sun turned into a black hole. Right now, things do crash into the Sun from time to time, increasing the mass of the Sun. On the other hand, there’s constant evaporation from the Sun’s atmosphere (as well as energy escaping in the form of sunlight, which translates into a mass loss via E = mc2). I’m pretty sure that the net effect right
now is that the Sun is gradually losing mass. Taken in isolation, this mass change would cause the Earth to drift gradually into a larger orbit.

That phrase “Taken in isolation” is important. There are other things that affect Earth’s orbit much more than this tiny mass loss rate. The main one is gravitational tugs from other planets, especially Jupiter. I
guess it must be true that the gradual mass loss of the Sun gradually makes all of the planets drift further out, although the details might be complicated.

There’s also the fact that the Earth is being bombarded by meteors. Those presumably slow the Earth down in its orbit. Taken in isolation, that effect would make the Earth spiral in towards the Sun.

I’ve never tried to work out the size of any of these effects. A lot is known about the effects of other planets’ gravitation on our orbit (the buzzword for this being Milankovich cycles). The other effects are much smaller.

Now, what would happen if the Sun became a black hole? Things like meteors would still get absorbed from time to time, but much less often than they do now. That may go against intuition, because we think of black holes as really good at sucking things in, but in fact the black hole has the same gravitational pull as the Sun on objects far away, and it’s a much smaller target, so fewer things actually hit it. So the rate
of mass increase due to stuff falling in will be less than it is now. On the other hand, stuff won’t be evaporating nearly as fast as it does now. (There would be Hawking radiation, but that’s incredibly small, much less than the rate at which atoms are boiling off the Sun now.) So the net effect would certainly be that the black hole would gradually go up in mass, whereas the Sun gradually goes down. The net result would be that the Earth would gradually get closer to the black hole.

But again, the key word is “gradually”: these are really really tiny effects. I’d bet that they’d be too small to have any noticeable effect even over the age of the Universe.

The Daily Show on probability theory

I liked this bit on the Daily Show about the Large Hadron Collider for a bunch of reasons, mostly because John Oliver is always great.  Among other things, though, it contains a great illustration of how tricky it is, when using a Bayesian approach to probability, to choose the right prior.  That bit starts at about 3:07 and is hilariously reprised at the very end, but you should really watch the whole thing if you haven’t seen it.

Since explanations of jokes are never tedious, there’s a bit of exegesis after the jump.

Continue reading The Daily Show on probability theory

Black holes in Slate

The online magazine Slate published a piece today explaining what happens to you if you fall into a black hole, and they had the good sense to consult me on it. Slate’s “Explainer” articles are also podcasted, so if you’re not into reading, you can listen to it instead.

The article pretty much gets things right. One minor quibble: the sentence

In fact, for all but the largest black holes, dissolution would happen before a person even crossed the event horizon, and it would take place in a matter of billionths of a second.

isn’t quite right: the “billionths of a second” number (which I think the author got from me) applies only to quite small black holes, not to “all but the largest” ones, and I think that even for stellar-mass black holes (which are much smaller than “the largest” ones) you’d make it across the horizon before being ripped apart by tidal forces. But those are pretty minor points; the main ideas are all right.

The motivation for this article is the possibility that the Large Hadron Collider will produce black holes. Short answer: It probably won’t, and even if it does, they’ll evaporate quickly rather than gobbling up the Earth. You really don’t need to worry about this.

Slate doesn’t do a lot of science reporting, but when they do it’s often pretty good. A recent article discussed one of the main things the LHC is actually expected to find, namely evidence for the Higgs mechanism. Unlike a lot of writing on the subject, this article actually tried to explain the fact that the Higgs mechanism won’t necessarily manifest itself as just a single new type of particle: it’s likely that something more complicated will be found. If so, that’ll be much more interesting than just finding a single Higgs particle.

Since I’ve been saying nice things about Slate, I want to end with one criticism of their science reporting: they still let Gregg Easterbrook write about science from time to time. Easterbrook’s done some good stuff over the years — in particular he was sharply and rightly critical of the space shuttle and space station long before that became fashionable, and he deserves credit for publicly and forthrightly changing his mind about global warming. (Also, I’ve heard his writing on the NFL is good, but I know nothing about that.) But as far as I’m concerned, anyone who defends the teaching of intelligent design in science classes forfeits all credibility as a science journalist. Yes, I’m intolerant and closed-minded about this. But I’m also right, so it’s OK.

Black holes

The section of my Black Hole FAQ on the observational evidence for black holes is sadly out of date, although the rest of it is still reasonably current. I don’t have any plans to update it, because that sounds altogether too much like work. I’d have to read a lot about things I don’t know much about in order to get up to speed on the subject, and if I’m going to do that, I think it’d be more fun to do it on some new subject rather than revisiting this one.

If I were going to write about this subject, though, I’d certainly want to talk about some recent results published in Nature concerning observations of the black hole at the center of our Galaxy. I think you need to be a subscriber to see the article or Nature’s newsy description of it, but there’s a Science News article that I think is publicly available. (Thanks to my brother Andy for pointing this out to me.)

There’s no way to see past the horizon of a black hole, so the name of the game in this business is to try to see as close as you can to the horizon. If you can resolve details near the horizon, you can look for distorting effects due to gravity, which provide pretty definite evidence that what you’re looking at really is a black hole. If all you can see is stuff that’s 1000 times bigger than the horizon, then it’s hard to tell the difference between a black hole and any other object of the same mass. The authors of this paper have managed to resolve structures that are just about the same size as the horizon.

By the way, one of the authors was a friend of mine in graduate school. Among his lesser-known accomplishments is writing a brochure describing the Berkeley astronomy department to incoming graduate students, in the form of Allen Ginsberg’s “Howl”. I don’t know if copies of it survive, unfortunately.

Some good web sites

Ned Wright’s Cosmology Tutorial: A great resource for all sorts of cosmology news and information.

Frequently Asked Questions about Black Holes (shameless self-promotion!)

John Baez’s web site, which is full of information about a lot of different topics in mathematical physics. The parts I’m most interested in are the ones about general relativity and gravity (and not just because I co-wrote some of it.)

For technical articles about astrophysics and cosmology, the place to go is the astro-ph arXiv.

For great astronomy pictures, you can’t beat NASA’s Astronomy Picture of the Day.

Update: These are now listed on the blogroll (over on the right), which is where they belong.