Do events inside black holes happen?

DR GABE PEREZ-GIZ: I'm sure you've read, seen, and heard a lot about black holes. Well, today, I'm going to try to make you rethink all of them, down to what the term "black hole" even means.

In today's episode we'll only talk about black holes from the perspective of classical general relativity. That means no Hawking radiation, no string theory, and no quantum anything—baby steps. Trust me, if I do this right, it'll be mind blowing enough. Now, it's a lot harder to say what I want to say about black holes if I make this video self-contained. To treat gravity Einsteinially rather than Newtonianially from the outset, it will help a lot if I can rely on technical terms like "geodesic" or "flat spacetime" and if I can draw a spacetime diagram or two. We all need to be on the same page with this vocabulary. So if you need a refresher, go watch our relativity playlist.

And finally, to minimise miscommunication, I need a favor from you. I need you to put your preconceptions about black holes aside and for the next few minutes, become tabula rasa and let me tell you a story about me, a pony, and a very acrobatic monkey.

Suppose that I'm very far from a black hole and there's a pony orbiting the black hole. She's close, but not that close to the hole. Don't worry. Fact: events that happen at a normal rate, as far as the pony is concerned, will happen in slow motion according to me. A day for her might be months for me. This is called gravitational time dilation, and the same thing happens around Earth, just to a lesser degree. Atomic clocks in high-altitude orbit will get ahead of clocks on the ground by a few microseconds each day, which is tiny, but GPS doesn't function properly if you don't take this into account.

OK. Now suppose that I send a tumbling monkey falling radially toward the black hole. As he tumbles on, I see his rotation rate become more slow motion, but I also see him pick up translational speed, just as I would if he were falling toward Earth. That is, until he gets really close to the black hole—see, eventually, the monkey will cross the black hole's edge without him noticing anything unusual. But that's not what I see. I see him weirdly slow down his progress until he's floating right outside the black hole's edge. At a certain point, I see him in suspended animation, not rotating, not progressing, just frozen.

And the pony agrees with me. So does another pony that's using powerful rockets to hover much closer to the black hole's edge. In fact, so would any observer, inertial or otherwise, who is always outside the black hole's edge. Even if the ponies and I were immortal, all of us would agree that the monkey's life just doesn't progress past this frozen moment.

The monkey knows he crosses the edge. I mean, he was there. But everyone else insisted he never does, even after an infinite amount of time on any of our clocks.

Do you get how freaky this is? The monkey is saying that certain events happen, but everyone else outside the black hole says that those events never happen, ever. In other words, there are apparently events that according to us out here cannot consistently be assigned a "when." From our frame of reference outside the black hole, those events just don't occur, even if we wait an infinite amount of time.

OK, you got all that? Here's the thing—a black hole is that set of events. According to observers like the monkey who are at those events, those events take place at spatial locations inside that black blob we see in the sky. But the blob, the black hole, is not just a set of locations. It's all the events that have ever or will ever take place there, according to observers who are physically there. The black hole is not a region of concurrent happenings with the outside world that the pony and I are just unable to see. It's not a visibility issue. Instead, the black hole is the collection of happenings that we say don't happen at all. And that black blob you see in the sky is just what it ends up looking like in ordinary spatial and temporal terms when you delete entire occurrences from every external observer's self-consistent record of the history of the universe.

By the way, for every particle that enters the black hole, some event on its world line is always the last event that makes it into my movie of the history of the world out at time infinity. OK, this final batch of events for all objects that enter that black void taken together is called the event horizon of the black hole.

The horizon is not just a spherical surface in space. It's not a shroud. It's a surface in spacetime. It represents the last events to which you can even assign a "when." So if a black hole is a bunch of events, then why do we talk about it as if it's an object? Here's why.

For simplicity of presentation, let's pretend that the Sun is a perfect sphere. It determines the spacetime geometry in its neighbourhood, the resulting geodesics of which correspond to things like radial freefall, orbits, et cetera. Now, if I replace the Sun with a spherical black hole that's around six kilometers across—and I'll tell you later how I got that number—the geodesics beyond where the Sun's edge used to be remain unchanged. Earth will freeze, of course, but its orbit won't be any different. So as far as Earth is concerned, that black hole generates the same spacetime geometry out here that the Sun does. In that respect, the black hole certainly behaves like an object, an object with the Sun's mass. So we associate one solar mass with the black hole itself.

In fact, if I give you a spherical object of any mass M, a spherical black hole with this special radius, called the Schwarzschild radius, will leave the spacetime that's originally external to that object unchanged. A black hole that mimics the Sun has a Schwarzschild radius of 3 kilometers. One with the mass of Earth would have a radius of just under 1 centimeter. But hold on a second. A black hole is a bunch of events. So is that collection of events somehow mimicking mass or does it actually have mass? Is there even a difference?

Hold that thought, because first, I want to debunk a few black hole misconceptions and then we'll come back to this question.

Misconception one, that black holes suck stuff in—they don't do that. They're not vacuum cleaners. You can orbit them just fine. I think this idea of suckage is rooted in a misunderstanding of the region that used to be inside the Sun but is still outside the black hole. See, spacetime geometry in this region is very foreign. For example, that is an allowed planetary orbit in that region. That region also has a cutoff radius inside of which there are no circular geodesics anymore. So a freefalling observer inside that cutoff, like the monkey, will go radially inwards. But it's not because he's being sucked in any more than the Earth sucks in a falling apple. He's just falling. As long as he stays outside the horizon, he can use rockets to hover or move radially outward just like on Earth.

Misconception two—black holes are black because not even light can escape their gravitational pull. That's not the reason, but here's my guess about how this unfortunate metaphor started. In Newtonian gravity, a projectile on the surface of a planet or a star needs a minimum speed called the escape velocity in order to get really far and not turn back as it's pulled by the planet's gravity. If a planet's radius equals the Schwarzschild radius of the equivalent-mass black hole, it turns out that the escape velocity is the speed of light. But that's just a numerical coincidence. In general relativity, remember, gravity is not a force at all. So even though it's true that everything inside a black hole, including a photon, will always move radially inward, it's not being "pulled." Instead, the insane curvature there has made geometry so weird that radially out is simply not an available direction. Loosely speaking, it's like being in an episode of "The Twilight Zone," in which no matter which way you turn, you're always facing inwards.

Now, that's really freaky, but it's not the reason black holes are black. Remember, from our point of view, there are no photons inside. A laser pointer carried by the monkey never enters the black hole, as far as we're concerned.

Because of time dilation, we would detect any laser pulse that the monkey sends with a lower frequency, i.e. a redder color, than whatever the monkey emits. So just before the monkey freezes from our perspective, the time dilation is so severe that any light he emits gets redshifted to undetectably low frequencies. That means that to external observers, black holes are black because light that gets emitted just outside the horizon is redshifted into invisibility. So even though my story about the monkey is correct, I shouldn't really have used the verb "see," because the infinite redshift keeps me from seeing him at all.

Misconception three, that all black holes are super dense—this kind of depends on what you mean by "density." If you mean that it's the black hole mass divided by the volume inside the horizon, then no. More massive black holes can have very low density. For instance, the 4 million solar mass black hole at the center of the Milky Way is about as dense as water. Strangely, the Schwarzschild radius criterion is based on circumference, not on volume. By the way, bigger black holes also have smaller tidal effects near their horizons. So even though a solar mass black hole would spaghettify you from pretty far away, you could enter a billion solar mass black hole completely unscathed.

But maybe that's not what you mean by "density." Maybe you mean that all black holes are infinitely dense because all the stuff that goes into the black hole collapses to an infinitely dense point called the singularity at the centre, right? Again, we have to be careful.

Misconception number three actually brings us full circle back to the mass question that I raised earlier. Astrophysically, a black hole can form when a sufficiently massive object, typically a very heavy star, collapses and becomes more compact than its own Schwarzschild radius. In this situation, the mass of the precursor star and the associated mass of the black hole will indeed be the same. However, the horizon forms first in the interior of the star and then expands. So to external observers, most of the matter never crosses the horizon. Remember, it's all frozen. So in this scenario, we can kind of sidestep the whole mass issue. To us, it's not inside the black hole.

But here's the problem. The Einstein equations also allow for an empty universe that has an eternal black hole that didn't form from anything, a spacetime that has an event horizon even though there's no stuff anywhere, including behind the horizon. This is the prototypical Schwarzschild black hole and I've always felt that whatever we're going to say a black hole's mass is the mass of, it should apply equally well to astrophysical black holes and to these idealised black holes. And in this circumstance, what are we supposed to assign the black hole's mass to? Remember, there's no stuff anywhere. So is the mass a property of the singularity?

Personally, I don't think that works. You see, the singularity also isn't a thing or a place or an event. It's like a hole that's been punched out of spacetime. So the geodesics terminate because there's no way for them to continue. So where's the mass? Is it associated with the curvature of spacetime, with all of spacetime? I'm not sure what the right answer is to interpretational questions like this or even if there is a right answer in vanilla general relativity. But this may just be my ignorance.

My goal today was just to correct some common misconceptions and to highlight some of the philosophical subtleties associated with thinking about black holes as "things." Of course, I've only scratched the surface of black holes. There's tons more to learn about them. There's rotating black holes, charged black holes, black hole evaporation, what goes on around black holes, how you form supermassive black holes, tons of stuff, some of which you might hear about, but from someone else.

Transcript ends at 11:30.