Yesterday and today on the BioLogos blog, we join physicist Aron Wall for a look into the thermodynamics of black holes. Aron began this two-part blog with a brief tutorial on entropy, which is helpful for understanding black holes in more detail. Today, we learn about singularities, distortions in spacetime, Hawking radiation, and more as a quick look into some of the more curious physical properties of the universe God made. (If you’d like to read more from Aron Wall, visit his blog).
Last time, I talked about how physicists like to count the number of possible configurations of matter systems. This gives us a number called the entropy, which is the thing that increases during irreversible processes (the Second Law of Thermodynamics). But there’s another sort of irreversible process out there, which has to do with gravity.
In our current best theory of gravity (Albert Einstein’s general relativity, the gravitational field consists entirely of distortions in space and time. Spacetime is an actual physical entity. It not only influences matter, it is also influenced by matter. Amounts of distance and time vary from place to place, similar to how the strength of the electric or magnetic field depends on where you are.
Any object with mass, such as the Earth, will slightly distort space and time in its vicinity. For example, time runs about one part in a billion times slower on the surface of the Earth than it does in outer space. (Believe it or not, this is what causes things to fall down!)
When a big enough star dies, one of the possible outcomes is that it collapses into a black hole. (There are also enormous black holes which form in the center of galaxies, which can have millions or even billions of times the mass of the sun!) Black holes are objects whose gravity is so strong that not even light can escape.
Because the paths of lightrays are distorted, anything that falls in past a certain surface (the event horizon), must inevitably fall in towards the center of the black hole (the singularity). You see, time is distorted so much, that once you cross the event horizon, progress towards the center is just as inevitable as progress from the past to the future.
All of the matter that used to be in the star gets crunched down to zero size in the singularity! As far as we know, time comes to an end for anything that falls into the singularity. But we don’t really know for sure, since our best theories of physics don’t work when you get too close to the singularity.
So you shouldn’t think of a black hole as being composed of any kind of ordinary matter “stuff.” It is composed entirely out of distortions in spacetime, i.e. the gravitational field. Similarly, the event horizon isn’t made out of anything tangible; it is just an imaginary surface in empty space marking the point of no return. If you fell across the event horizon, you wouldn’t hit any object as you crossed; it’s just empty space.
Now let me clear up a common misconception. A lot of people think that once a black hole forms, it would start sucking everything nearby into it like a vacuum cleaner. This isn’t quite true. A black hole doesn’t have any more gravity than anything else of the same mass at the same distance. If the sun collapsed into a black hole next Tuesday (which can’t really happen—it’s too small a star—but let’s just suppose) then the orbit of the Earth would remain exactly the same.
But if you drop things in close enough, they will get eaten. Like people, black holes grow bigger when they eat things. In fact, the radius of their event horizon is proportional to their total mass. This is where the irreversibility is going to come in—black holes get bigger, but do they ever get smaller?
In 1971, Stephen Hawking mathematically proved an “Area Increase” theorem based on the equations of classicalgeneral relativity. (In physics lingo, “classical” means not taking into account quantum mechanics.) Hawking showed that the surface area of a black hole’s event horizon can only increase as time passess—it can’t get any smaller. Similarly, if you merge two black holes into each other to make a single black hole, the total area of the result has to be greater than the sum of the original two.
This led Jacob Bekenstein to propose that black holes actually have an entropy which is proportional to their event horizon. Remember that the Second Law says that the entropy always has to go up. Bekenstein’s proposal was based on an analogy between the behavior of matter systems (whose entropy increases) and the behavior of black holes (whose area increases).
At first everyone thought that Bekenstein’s idea was ridiculous. After all, if black holes really work the same way as ordinary thermodynamical systems, then they’d have to have a nonzero temperature. If you put a hot thing next to a cold thing, heat flows from the hot object to the cold object. That means that a black hole in empty space (which is at absolute zero) would have to emit radiation. But everyone knew that nothing comes out of a black hole.
It turns out that everyone was wrong. Once you take into account quantum mechanics, black holes do radiate particles just like a thermal object. This was shown by Stephen Hawking in 1977 just a few years later. Although nothing can escape from inside the event horizon, this “Hawking radiation” emerges from just outside the event horizon. The larger the black hole, the colder its temperature. In principle, any kind of particle could come out of a sufficiently small, hot black hole. But for a solar mass black hole the Hawking temperature is very tiny (10-7 degrees above absolute zero), and there is only enough energy to radiate massless particles (photons and gravitons), in radio wave frequencies. Unfortunately, the number of Hawking photons emitted is so small that detecting them would be quite hopeless, even if we had a measuring device right next to the black hole.
As the black hole emits radiation, it loses energy and very slowly shrinks. So Hawking’s theorem doesn’t apply; the area decreases. However, it turns out that the radiation which comes out has even more entropy than the black hole did. No matter what you do, the total amount of entropy always goes up. So it seems like black holes obey the Second Law even when you take into account quantum mechanics.
Now we come to the surprise twist. Event horizons seem to have entropy, yes, but no one knows what the entropy is counting! In ordinary matter systems, the matter counts the number of ways for the matter atoms to be arranged. But black holes aren’t made of matter, they are made of spacetime. By analogy, the entropy of the black hole probably tells us the number of possible configurations of whatever ingredients spacetime is made out of!
The size of the black hole entropy suggests that these ingredients are probably about 10-35 meters in size (Planck length). This is about 20 orders of magnitude smaller than a proton or neutron. So it is not surprising that space and time seem continuous to us at human scales. But when you get small enough, they may really be made out of little chunks that can’t be subdivided! But there’s no way to do experiments to measure distances that small, so we can’t know for sure what’s going on. But we’re grateful for every tantalizing clues we can get.
God could have chosen to tell us what are the laws of the universe. But he didn’t. Instead He allows us to gradually find out what they are. There’s a certain thrill to knowing how things work, but there’s also a sense of sublime wonder when you come to the limits of our understanding. I love thinking about quantum gravity because one continually comes up against these deep mysteries. Glory be to God!