Posted on August 20, 2004

Soapbox Seminar #6

Beyond the Black Horizon

When we left off last time, we’d just got done scrunching several suns’ worth of mass down into what we called a “singularity.”

Now, calling something a singularity is just a polite way of saying it’s impossible. Whenever an equation breaks down and starts churning out meaningless results — infinities and the like — well, physicists find that real “singular.”

It turns out that Einstein’s theory of relativity suffers just that kind of breakdown when it tries to describe what goes on inside a black hole. In particular, the field equations predict that what we’ll find at the center of the hole is a dimensionless point of infinite mass, infinite density, infinity curvature, infinite whatever. In short, a singularity.

All this is really bad news for modern physics. And I don’t just mean the part about the tensor calculus spitting out impossibilities. No, all kinds of bad things go on in Mr. Singularity’s Neighborhood. General Relativity says that gravitation is equivalent to acceleration, you see, and that enough acceleration will do really weird stuff to time and space. So an infinite gravitational field is something physicists would just as soon not deal with.

Luckily enough, we mostly don’t have to. Because there’s a silver lining to this particular black cloud: namely, that singularities just naturally wall themselves off from the rest of the universe.

It’s called an “event horizon.” You could think of it as job security for physicists. It’s there to make sure that all the paradoxes riddling the inside of a black hole can never get out to pollute the universe at large.

Now, for something so simple, this event horizon idea has stirred up an awful lot of confusion. Sometimes you’ll hear people talk about it like it was a physical barrier or something. There’s even a Star Trek: Voyager episode (the one called “Parallax”) where Voyager escapes from a black hole by scooting through a “crack” in the event horizon!

That episode won a place of honor on Lawrence’s Krauss’s top-ten list of all-time Star Trek bloopers. Because, with apologies to Captain Janeway, the whole notion is just plain silly. It’s not like an event horizon was the sort of thing that could develop a hairline fracture. In fact, it’s not a physical object of any kind, no more so than that old, familiar horizon we watch the sun set behind every day.

With one big difference: you could walk forever and never reach the horizon here on earth, whereas it’d be all too easy to reach, and cross over, the event horizon surrounding a black hole.

Because what an event horizon really is, is just the mathematically-defined dividing line (dividing sphere?) between a singularity and the rest of the universe. It’s the point — the collection of points, actually — of no return. Cross it, and there’s just no turning back. Not even for a beam of light.

Why is that, exactly? Well, imagine you’re trying to climb a ladder out of a really, really deep hole. Doesn’t matter if you go fast or slow; as long as you keep climbing, you can’t help but make it eventually — or so you think.

Now, it’s going to be a long climb, so you’re going to want to bring some food along and stop every now and again to have a snack. Let’s say you go up a mile, then take a Snickers break. That gives you the strength to keep going.

But what if the pull of the gravity you’re fighting against is really strong, so strong it takes more energy to lift that candy bar a mile than you’ll get back by eating it? That makes your Snickers break a losing proposition — you’d have done better to leave the food at the bottom.

Of course, your average candy bar’s pretty heavy, compared to its nutritional value. You’d be a lot better off with something you could turn completely into energy — a candy bar, say, where the ingredients label reads “chocolate, sugar, almonds, anti-matter.” Makes no never mind, the total energy content’s still finite. If the gravity’s strong enough and the ladder’s tall enough, you’re still going to wind up burning more energy lifting that anti-Snickers than it can possibly give you back. Meaning that, at some point short of the top, you’re just plain going to run out of steam.

Even so, it’s not like gravity’s crushing you to the floor. You can still climb. You just can’t climb all the way to the top. All the gravity in the universe won’t slow light or hold it back — but it can rob it of energy. Partway out of the hole’s gravity-well, it just runs out of energy and ceases to exist! And light’s pure energy, no excess baggage. If it can’t make it, neither can anything else.

So whatever falls into the hole can’t ever “talk” to anybody on the outside ever again. A careless experimenter that slips and falls in can’t tell us what his instruments read. And, considering how weird things can get down at the singularity, that’s a good thing.

Other than that, though, there’s really nothing there. With a large enough hole, billions or trillions of solar masses, you could cross right over the event horizon and never notice the difference. Until you realized you couldn’t get back out again, that is. Once you’re trapped inside an event horizon, all roads lead downward, to the singularity.

Meanwhile, precisely because nothing can get ever out, black holes as seen from the outside are really simple objects. It doesn’t matter what the matter that went into them was in its previous life: Two or three solar masses worth of used TV sets’ll do just as well as the same weight of lottery tickets or butterflies or (in the case of a supernova) stellar core material. Or anti-matter, or pure energy, even. The end result is always the same. All that the final collapse leaves behind is mass and, optionally, spin and/or electromagnetic charge.

And that’s it. As Princeton physicist John Wheeler put it: black holes have no “hair” — no other distinguishing traits. Like a prisoner of war dead set on giving out no more than name, rank, and serial number, a black hole will tell you its mass, spin, and charge, but nothing else.

(Well, and maybe not. Stephen Hawking has just come out this summer with some new work that threatens to upset the applecart once again. Seems quantum fluctuations at the event horizon may cause a hole to eventually regurgitate, in a “mangled” form, all the matter it’s ever swallowed. The jury’s still out on this one, though.)

But even given only mass, spin, and charge to work with, black holes can still conjure up some mighty strange effects. Like frame drag, for instance. That’s where a spinning black hole pulls space itself along behind it in the direction of its rotation.

Or, my personal favorite, the tides.

Because tides are nothing but a gravitational effect. Think about it this way: the moon’s gravity pulls on every atom of the earth. But that pull varies with distance. The atoms directly beneath the moon feel it strongest because they’re the closest, so they get dragged up toward the moon, away from the bulk of the planet. Those on the opposite side of the world, the ones furthest away, are getting pulled on the least, so they get left behind, relatively speaking. The upshot is: the whole planet gets stretched a little.

Now, the solid body of the earth itself is reasonably rigid, so it stays more or less round no matter how it gets pulled on. But the oceans are a different story; they get stretched out into an ellipsoid, with a bulge at either end. What that gives you is two standing waves of seawater moving through the oceans at twelve hour intervals as the earth rotates beneath them. In other words, the tides.

With me so far? Then add this: That tidal effect isn’t peculiar to earth. It happens everywhere there’s a gravitational field. And the more intensely that field’s strength changes with distance, the higher the tides become. Get in really close to a singularity and its gravity gradient can produce tidal distortions across distances measured in micrometers or less. An object would need phenomenal tensile strength to survive a fly-by. As for a human being, you can forget about it! Come in too close, and you’d be stretched out like a piece of saltwater taffy — torn limb from limb, then atom from atom.

Bad as all that is, we can take some comfort from the fact that the event horizon is always there to shield us from even worse.

... Or is it?

[Notes and Further Reading]

Mitchell Begelman and Martin Rees, Gravity’s Fatal Attraction: Black Holes in the Universe, Scientific American Library, 1996.

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