Black holes

Black holes are well understood by physicists, but I’ve read too many oversimplified, confusing, and seemingly-contradictory descriptions of them. Over time, I’ve settled on my preferred mental model of a black hole, one that usually helps me to work out the right answers to questions that non-physicists have about black holes. (An example of such a question: What would happen if you escorted a small black hole into a large black hole?) In this post, I’ll try to explain that model.

For simplicity, I’m going to assume a non-rotating black hole, even though black holes naturally rotate. Non-rotating black holes are hard enough to figure out, and rotating black holes can be much worse.

The orthodox model

The usual description of a black hole goes something like this: “A black hole is the remains of a star that underwent gravitational collapse. It is a singularity of zero volume and infinite density. It lies at the center of an event horizon that surrounds it, and anything that touches the event horizon will inevitably be pulled into the singularity.”

We may be given a diagram similar to the one below, showing a black disc. The black disc may or may not be labeled as the event horizon, but even if it’s not labeled, we are obviously going to assume that it represents the event horizon.

My model

A black hole is an object that has undergone gravitational collapse, and occupies a spherical region of space. (It may have once been a star, but a black hole is a black hole regardless of how it formed.) At its boundary is an event horizon. Anything that touches the event horizon cannot escape from it. But, whether there is anything inside the event horizon depends on your perspective.

To be clear, whenever I talk about the size of a black hole, I mean the apparent size of the region subtended by its event horizon. The inside of a black hole is the part that is beyond the event horizon.

For any given spherical region of space, there is a maximum amount of mass that it can contain. If you put that amount of mass into such a region (for long enough for gravity to propagate through it — usually a fraction of a second), it will become (maybe a better word is “be”) a black hole. You cannot put any more mass into it, because if you try, the black hole will get bigger, and will no longer fit into that region of space. Incidentally, it’s not that there is a universal maximum density. The smaller the region of space, the more densely it can be packed with matter.

One cannot satisfactorily explain black holes without first taking a detour to emphasize that perspective really matters. It’s not just that the black hole looks different from different perspectives, it’s that reality itself is different, especially if an observer has crossed the event horizon.

A distant observer

For this section, assume the observer is outside a black hole, a good distance from it, and approximately stationary relative to it. From this observer’s perspective, the black hole has no interior. There is nothing inside it, not even empty space. It is literally a hole in space. It is reasonable to say that the black hole is its event horizon.

At a certain distance from the event horizon, there is an imaginary boundary called the photon sphere. Its radius is 1.5 times the event horizon’s radius. Any photon, or any object in free fall, that touches the photon sphere from the outside will (unless it is interfered with) also touch the event horizon.

We assume that most of the time, there will be no objects inside the photon sphere emitting significant light, so the photon sphere looks like a black disc.

I envision the cross-section of a black hole to be something like this:

If you’re surprised that the black disc is not the event horizon, well, it’s not that simple. Light emitted from just outside the event horizon will have its path warped by gravity so much that it can appear to be coming from anywhere in the black disc. Essentially, gravitational lensing causes the event horizon to be magnified so that it appears to have the same size and position as the photon sphere. So, it’s not wrong to think of the black disc as the event horizon, but I don’t think it’s the best way to think about it.

Incidentally, the laws of physics don’t forbid objects other than black holes from having photon spheres. It’s conceivable that some neutron stars have a photon sphere. The experts don’t seem to have figured out whether this actually happens.

I have yet to say anything about a singularity, and that’s because, from this perspective, the ever-popular singularity at the center of the event horizon does not exist. As I said, there is nothing inside the event horizon. But I don’t want to claim that a black hole does not have a singularity, because really, the event horizon is a singularity: It’s a place where something goes to infinity. It’s just not point-like.

When I assert that the point-like singularity does not exist, I am using a fairly strict definition of the concept of existence. By this definition, in order for something to exist, it must be observable, at least in principle. But the singularity is not observable, even in principle, from outside the event horizon (and not really even from inside it). Even given arbitrarily advanced technology, you cannot design an experiment that will demonstrate its existence to observers outside the event horizon. It is not part of the observable universe. The math may say that it exists, but that’s using a different (and I’d say less useful and meaningful) definition of existence. Think of the clues given by quantum mechanics and Schrödinger’s Cat: Things are not fully real until they have been observed.

Traveling inward

Suppose we inexplicably decide to dive into a black hole. We’ll assume it is a supermassive black hole, millions or billion of times the mass of the Sun. It has to be big, so that we can approach and cross the event horizon before being torn apart by tidal forces. We get in our spaceship, and free fall toward the black disc of the black hole.

Due to gravitational lensing, the black disc does not actually block out any of the stars behind it. Some of the light from those stars still reaches us, as gravity bends it around the disc. The entire sky is visible.

As we fall, the black disc appears larger and larger, but nothing special happens when we cross the photon sphere, or the event horizon. Shortly after that, we’re torn apart by tidal forces.

Distant observers watching us see us squished onto the event horizon. In theory, the light from our last few moments outside the horizon gets stretched out so much that we never disappear. But in reality, our image quickly fades to invisibility.

I should mention the “firewall” theory. Some physicists hypothesize that there is a weird quantum mechanical standing wavefront, or something like that, that will vaporize you as you cross the event horizon. I am not qualified to offer an opinion as to whether this is plausible, and I don’t even know what perspective(s) it applies to. I’ll just assume there’s no firewall.

Now let’s rewind time, and try a different approach. We’ll give our spaceship an arbitrarily powerful engine, and use it to descend very slowly into the black hole.

In this case, the black disc appears bigger than it did in free fall. If we have a powerful telescope, and use it to observe the universe behind us, we see that events appear to be happening more quickly than they normally do, as if time were sped up. We are traveling into the future.

When we reach the photon sphere, the black disc covers fully half of our sky. Descend a little further, and the black disc covers more than half of the sky. The black disc now is our sky, and the rest of the universe is an ever-shrinking starry disc. Though the starry disc is shrinking, it still contains the same number of stars, compressed into it.

The starry disc continues to shrink as we descend, and we have to put more and more power into our rockets just to keep descending at the same slow speed. If we’re feeling a bit uncomfortable at this point, our feeling is well justified. We can still escape, but the universe is being pinched off from us, and the path back to it is getting very narrow. When the starry disc shrinks to a point, it means we’ve reached the event horizon, and can never get back to the universe, no matter how powerful our engines.

After we cross the event horizon, I’m less confident that I understand what we’d observe. It is sometimes said that, beyond the event horizon, “time and space switch roles”. So, yeah, I hope that clears it up. I think the outside universe is still visible as a point of light, and that we could get a better view of it by accelerating inward, though of course that won’t save us.

We are now literally in another universe, separate from the universe we left. Or, maybe more accurately, we’re falling through an infinite sequence of concentric universes. In some sense, we’re in the infinitely distant future of the universe we left.

You might think that our observations of the black hole’s interior contradict my earlier statement that black holes do not have interiors. And you’d be right. But reality sometimes allows contradictory things to both be true, provided that it is impossible for a single observer to observe both of them. This sort of thing doesn’t happen in everyday life, but it does happen with black holes, and that is a big part of the reason they are hard to understand.

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