Friday, January 31, 2020

Black Holes are a Thousand Times Weirder than You Think

In the depths of space, there are objects that undermine everything we feel we know about space and time. These objects are black holes.

A realistic depiction of what a black hole would look like up close, using the universe simulator Space Engine.

A black hole forms when an amount of matter is squeezed smaller than its Schwarzschild radius, the size at which its gravity is so strong that nothing, including light, can escape. When this happens, an event horizon forms at the S-radius, and the matter inside collapses to form a singularity. We’ll get a feel for what these mean as this post goes on.

The incredible amount an object must be compressed to form a black hole is staggering. In order to turn the sun into a black hole, we would have to crush it down to 6 kilometers across. That’s the total distance I walked every day to and from my university when I was in graduate school. If you were to compress the Earth into a black hole, it would be the size of a marble. If you didn’t have to worry about it tearing you apart, you could hold it in the palm of your hand.

Why do black holes look the way they do? Let’s start with a lone black hole in the cold depths of space. Since light can’t escape, it looks like a circle of blackness, and because the strength of their gravity is so great that they bend light around them, they distort the stars behind them like a lens.

From the YouTube video, “Colonizing Black Holes,” by Isaac Arthur

When a black hole is feeding on material around it, perhaps from a companion star or an object that came too close to it and was torn apart, it gets an accretion disk. Why does a disk form, rather than all the matter just falling in? There are two reasons working together. First, we have angular momentum. The matter isn’t falling straight into the black hole, but orbiting around it at insanely high speeds. Because of this, any stray matter that collides with the disk becomes part of the disk. Secondly, as the matter gets closer to the black hole, it crams together and can only go in so much at a time, like sand trickling through an hourglass.

An artist's impression of an accreting black hole. From Wikipedia

We can see an example of angular momentum creating a disk in the above artist’s rendition of a black hole accreting matter from a companion star. The star and black hole are revolving around each other, so the stream going from the star to the accretion disk curves in the forward direction, partially because of the star’s inertia, and partially because the black hole moves out of the way and the stream has to catch up.

With all that matter spiraling inward, feeding black holes build up quite the magnetic field. This magnetic field points outward from the poles, so instead of falling into the event horizon, some of the matter gets shot away at extreme speeds by these magnetic fields in two jets, as can be seen in the above picture.

As the matter in the disk crams together, it heats up due to friction, which causes the accretion disk to glow. The closer to the center, the hotter it gets, making it go from red on the outside to white on the inside. Because of how fast it is revolving, the light gets Doppler shifted, brighter and whiter on the side moving toward us, and dimmer and redder on the side moving away from us. This is heightened by the fact that the disk is spinning close to the speed of light.

A realistic depiction of a black hole up close, from the movie, Interstellar

You might notice that there is a halo around the event horizon. That’s an illusion, an image of the accretion disk on the back side of the black hole, which we can see both above and below it because of the light bending around the event horizon.

Up until 2015, we didn’t have direct observations of black holes. Now we do, first by gravitational waves with LIGO, and then a few years later by the Event Horizon Telescope, a composite telescope that uses advanced techniques to put together data from observatories all over the world, giving us an effective dish size as big as the entire Earth. Here is what that image, given artificial color, looks like.

The supermassive black hole at the center of galaxy M87.

The black circle in the center is the shadow, a blown-up view of the entire event horizon, front and back, because of the way light bends around it. If you could see it without any lensing effects, the event horizon would be a fraction of its size. There is a great YouTube video by Veritasium explaining this in more detail.

Black holes look cool, and a lot of interesting science goes into why the look like they do. But there’s more, oh so much more. So now it’s time to get to the good stuff: what black holes do to space and time. In order to discuss this, we have to be comfortable with space-time relativity, the principle that space and time are parts of the same thing, and this space-time can be curved and stretched. We talked about this in our discussion of faster-than-light travel and time travel, but here’s a little refresher.

When drawing space-time diagrams, we draw one dimension of space on the horizontal axis, and time on the vertical axis. An object sitting still will move straight up on the diagram, parallel to the time axis. An object moving will travel at a diagonal angle. We scale the plot so that light beams travel at 45-degree angles.

We choose a point to be the origin of the plot, which we call “here and now.” This could be you, it could be a space ship, a rock, or just a random point in space-time. From this point, we draw the light beams that go out into the future and come in from the past. If you imagine a third axis pointing out of the screen, these light beams circle around the time axis, making cones, which we call the past and future light cones. In reality, there is also a third dimension of space, making it a hypercone, but it is very hard to visualize four dimensions, so we talk about light cones.

From Wikipedia

No matter where you are or what the space-time curvature around you looks like, your light cone looks like this diagram. But someone else’s light cone at a different point in space could be distorted compared to your coordinate system. For instance, if we are in normal space far away from a black hole, then the light cone of something falling into a black hole curves to point toward the event horizon. And after an object has passed the event horizon, its entire light cone points toward the singularity. There is no direction it could go that would not end up at the singularity.

This is confusing, and not good for calculating. A much better and more intuitive way to understand black holes is with a Penrose diagram. To make a Penrose diagram, we use a math trick to change our coordinates so that we compress all of space-time into a diamond. The two bottom edges of the diamond are infinitely far back in time, and the top right is where time reaches future infinity. The top left is the event horizon of the black hole. On the other side of the event horizon, we join another half-diamond, representing the inside of the black hole.

In this diagram, lines of constant position and constant time are curved. Yet light always moves at 45-degree angles, making it easy to tell what observers in each region would see. Imagine two people, person A staying outside, person B falling in, sending signals to each other. To A outside, it would take an infinite amount of time for B to reach the event horizon, and A could keep receiving signals from B forever. However, in B’s reference frame, B passes the event horizon in a finite amount of time no problem. Then, a short time later, B reaches the singularity. Contrary to popular myth, B does not see the entire future of the universe, as we can see from the following diagram.

The paths of A and B exchanging light beams as they go. Everything moves upward, because that is the direction of time. As we can see, once B passes the event horizon, their light beams end at the singularity. B can receive signals from A, but there comes a point when A’s signals reach the singularity without reaching B first.

With a Penrose diagram, we can see a startling conclusion: inside the black hole, space and time have switched places! The singularity is no longer a point in space, but a moment in time, which all things inside the event horizon move inexorably toward. In addition, according to an observer outside the event horizon, everything that happens inside takes place after an infinite amount of time has passed!

Have a moment’s rest before we continue on. What, did you think that was as crazy as it gets? We haven’t even gotten to wormholes yet.

To get there, we first have to talk about spin. Everything floating in free space has a little bit of angular momentum, its outer parts rotating around its center of mass. Black holes are no different; the matter that forms and feeds them spirals in, contributing to their angular momentum. As a result, black holes have a property called spin. This spin prevents the matter from falling all the way to a single point, as the closer it gets the more centrifugal inertia it has to counteract the gravity. What this means is that the singularity is not a point, but a ring of zero thickness. If the spin is so high that the radius of the ring is larger than its Schwarzschild radius, then there is no event horizon, and it is called a naked singularity. Currently, no naked singularities are known to exist.

A simulation of what a naked singularity would look like from above.

If mass distorts space-time, do black holes pull space around them as they spin? Yes, they do. It’s called “frame dragging,” a name as cool as the phenomenon it describes. If we were to drop something directly toward a black hole near its plane of rotation, it would spiral around the black hole as it fell, due to the motion of space itself. There is a region near the event horizon called the ergosphere, where space is pulled so fast that an object has to travel faster than light in the opposite direction just to stay in the same place. The ergosphere is outside the event horizon, so in principle it is possible to send a ship or a probe into it and back out again. Now that would be a trip!

From Wikipedia

All right, now we’re ready to get to wormholes. Since black hole singularities are rings, it stands to reason that it’s possible to go through it. What happens? Well, you might think you just end up on the other side of the ring. After all, that’s what happens when you pass through any other kind of ring. But something weird happens. When you were a child, did you ever imagine you could go around a lamp post or a tree and find yourself somewhere else? That’s what happens when you pass through a ring singularity. Let’s look at the Penrose diagram:

With a path through the singularity, we can see that there is another side. When we get there, instead of the other side of the black hole, we find something called a white hole, an object with repulsive gravity and an event horizon nothing can get into. No one knows if white holes exist, and we don’t know of anything that has repulsive gravity. Thus, we have a one-way wormhole, with a black hole on one side nothing can get out of, and a white hole on the other side nothing can get into. What is on the other side? It could be a different place in the universe, maybe at a different time. Or, it could be another universe altogether, a space-time continuum completely separate from ours except for this one bridge.

We have never seen a white hole. This does not bode well for the possibility of their existence, since they would probably be extremely bright, launching out everything that fell into their black hole partner at relativistic speeds. Except, well, maybe we have. There is one thing that had a singularity and looks kind of what we’d expect a white hole to look like: the big bang. It’s common to think of the big bang as the beginning of everything, including time, but it might not be. Maybe it was the result of a black hole in another universe. This may seem like nothing more than sci-fi fancy, but there are a few high-profile physicists who take the possibility seriously.

So there we go, a glimpse into the depths of the weirdness of black holes. There is one more thing I’d like to say: we don’t actually know much about singularities. When we try to apply our best theories to them, General Relativity and Quantum Field Theory, we get unsolvable problems. In order to be able to model singularities, we need a theory of quantum gravity. Our two major contenders, String Theory and Quantum Loop Gravity, have both made predictions that turned out to be false. So the final tidbit of black hole weirdness I’ll leave you with is that there is still a feature about them, the singularity, that we know basically nothing about. I hope you sleep well tonight. See you next time.

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