The several styles of singularities

23:17Get your friends and grab tickets now at creditunion1amp.com. Hey everyone, it's Cal Penn, host of Earsay, the Audible and iHeart Audiobook Club. This week on the podcast, I'm sitting down with Will Wheaton, who played Gordy Lachance in Stand By Me 40 years ago and now narrates Stephen King's The Body, the novella that inspired it all. We talk about what it's like to return to a story that shaped his life, channeling his memories of River Phoenix in the recording booth, and why the friendships you have at 12 might be the most important ones you'll ever have. I know Gordy Lachance. I am Gordy Lachance.

23:58Like, I mean, even when I was a little kid, I was Gordy Lachance when I didn't know it. Listen to Earsay, the Audible and iHeart Audiobook Club on the iHeart Radio app or wherever you get your podcasts. The following ad is sponsored by Pets Best Insurance Services. You knew right away, he's perfect. The one for you. Those puppy dog eyes, that cute little button nose. You don't even mind the drool. When you find your perfect match in a dog or a cat, the love is unconditional. Your budget, on the other hand, has realistic limits. Help protect your heart and your wallet with pet insurance from Pets Best.

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25:21all right i've recovered from the wicked burn daniel gave me regarding my driving skills you're the one who said you drive into singularities well i i said well mate what happened yeah maybe i did all right you got me all right tell me about black hole singularities let's stop talking about my driving record all right so we have this concept of spatial curvature and it explains the effect we call gravity. And so what happens near massive objects is things move towards those massive objects because that's where the curvature of space is. And a black hole is an example of that curvature growing so powerful that light becomes trapped inside that curvature because the direction of space is just 1D inside that black hole.

25:59Beyond the event horizon, space is curved so much it only points towards the core. And at the core, according to the calculations of general relativity, that curvature becomes infinite, right? So the courager of space itself becomes infinite. So like, what does that mean? Well, if you have two points on the opposite sides of a black hole, what is the distance between them? If it's going to pass through the singularity, that distance is infinite. So is this a case where the equations are breaking down and, or is this like actually what we expect will happen? Yeah, that's a great question. My suspicion is that the equations are breaking down because what we've done here is extrapolate general relativity beyond the point of its relevance.

26:38We're doing a calculation in general relativity and we're ignoring quantum mechanics. And most of the time you can do that. When you're calculating how two black holes are going to fall into each other or how Jupiter moves around the sun, you can ignore quantum mechanics. It doesn't really matter. The same way you can ignore gravity when you're doing quantum mechanical calculations on individual particles. But when you're talking about super tiny, dense objects, like at the heart of a black hole, quantum mechanics matters again. Quantum mechanics says that that prediction is wrong. It can't happen.

27:07You can't have that much mass isolated with that much energy in that small space. It violates the Heisenberg uncertainty principle. It definitely would not happen. So what you've done here is taken general relativity, ignored quantum mechanics, but done it in a region where quantum mechanics can't be ignored. So it's, in that sense, kind of a nonsense prediction. It's also sort of a useful diagnostic to say like, well, is general relativity valid here? I think this is the universe telling us no. So quantum mechanics says it can't happen. General relativity says it does happen. We don't have a great theory of quantum gravity to make these calculations.

27:39And so it's sort of a question mark. Is this level of nuance conveyed in like pop culture treatments of black holes? Or how is this usually conveyed in pop science? Most of the popular science treatments just say that there's a singularity, the heart of the black holes, but scientists don't understand it. I think more often we should underline that this is a prediction of a classical theory, and we already know that classical theory is limited and that we shouldn't trust its predictions. That doesn't mean you shouldn't make those predictions and use them again as a diagnostic. But I think some of that nuance is missing.

28:12Okay. And what do experiments tell us about whether or not this is where things are breaking down or if we're really describing the universe? Experiments have been really influential in our understanding of black holes. Originally, this whole idea, people thought, well, it's ridiculous. There's no way the universe is going to let a black hole form. Not to mention even like, is there a singularity at its heart? But do black holes exist at all? For a long time, they were just like a curiosity of the math. And people were like, well, this is definitely a sign that something is wrong and the universe would never let this happen.

28:40But then we found things that look a lot like black holes that are very, very dense and very, very massive and have incredibly powerful gravity on the things near them. We see them at the hearts of galaxies. We see them where stars have collapsed. Do we know that these are actually black holes that have an event horizon and potentially singularity within them? Not technically. We have only indirect evidence that these things are black holes and that there's nothing else in our physics that is so massive and so dense and so compact all at the same time. They can't be neutron stars. They can't be white dwarves.

29:12They can't be anything else in our physics. So the only thing left in the box is a black hole. But there are other ideas out there of things that they could be. String theory predicts things like fuzzballs. There are other quantum versions of these predictions. So we have only indirect evidence that black holes actually exist, even though they're treated as like definitely existing and having been observed in the sort of broad popular literature. Yeah. And I really enjoyed our recent conversation about Bechdel stars and black holes are confusing, but we're learning more all the time. Yeah. And that's not a criticism of astronomers.

29:44Like it's amazing what they found and, you know, seeing black holes is hard. And even the Event Horizon Telescope, which is image, the accretion disk around the black holes tells us a lot, but isn't a direct observation of the event horizon itself. Right. Okay. So we've talked about black hole singularities. Right. Are there other kinds of gravitational singularities to talk about? Well, all the singularities we're going to talk about, which makes me think of Beyonce. Oh, the singularities. Are at the hearts of various kinds of black holes. Okay. And so let's catalog those. The sort of vanilla singularity, the classic one, is at the heart of a black hole that's very simple.

30:24It's spherical, it has a lot of mass, has no spin or no charge. Remember that the kinds of things a black hole can have, according to general relativity, are just three. There's only three things you can know about a black hole. It's mass, it's spin, and it's charge. You can't know anything about how those things are arranged within the event horizon, and you can't measure any other physical properties. So those three things completely determine the black hole, again, according to classical general relativity. So if you have the simplest kind, which is a short-sized black hole, just a really massive stuff with no spin and no electric charge, then you get an event horizon that's spherically symmetric.

31:01And at its heart is that point, that singularity, the location of infinite density or infinite curvature. And that's the sort of vanilla classic singularity that I think most people think about when they think about black holes and singularities. Okay, sorry, I'm still absorbing. Okay, so these are all examples of stuff at the middle of a black hole and just differences in the way that we think about them. Yeah, exactly. And these characteristics of the black hole determine what's happening at its core. So if you just think about a lot of stuff, a star collapsing into a very dense object, that's a Schwarzschild black hole.

31:33And that was the first solution to Einstein's equations ever found to describe a black hole. No spin, no charge, just mass. All right. I think it would be pretty awesome to have a type of black hole named after yourself, but that's probably not going to happen for me. But all right. So we've got Schwerstein, if I could say it. We've got the first kind of black hole we talked about. Okay, so we're going to be looking at variations on mass spin and charge. Our next kind has what? Spin, right? Okay. It's very unlikely that something collapses into a black hole and isn't spinning. Why? Because everything in the universe is spinning.

32:09All the stars out there are spinning. All the galaxies out there are spinning. Everything is spinning. And the reason everything is spinning is the reason we have any structure at all. You started with vast clouds of hydrogen, but then you had little regions of over densities and under densities where gravity took hold and gathered stuff together and collapsed it. And overall in the universe, we think there's probably no spin. But if you take a random region of the universe, there's going to be, on average, a little bit of spin. It's like taking a million coins and flipping them and saying, do you get exactly 50 % heads?

32:39No, you get a little bit extra tails sometimes or a little bit extra heads another time. If you randomly chop the universe up into chunks, each one's going to have a little bit of spin. They all add up to zero, but each one's going to have a little bit of positive, a little bit of negative spin. It's not impossible to have zero, but most likely it'll have non-zero spin. And then that collapses into stars and gets exaggerated because as things collapse, they spin faster, like a figure skater pulling in her arms. So if you have a star, it's most likely spinning. When it collapses, where does that spin go?

33:09Well, it can't just go away. Spin is conserved in the universe. And so a spinning star has to turn into a spinning black hole. So I think that most of the black holes in the universe are not short-sized black holes. They're curved black holes. They have mass and spin. And so they're called curve black holes? Curve, K-E-R-R for the New Zealand physicist who came up with them. Ah, all right. Curve black holes. Okay. So you wrote ringularity. What does ringularity mean? Yeah. So what is at the heart of a spinning black hole? Well, it can't be a singularity. Why not? Because a singularity, a point, can't have spin.

33:47Oh. Right? If you have something which literally has no extent, then it can't spin. There's nothing to spin. And so what's at the heart? How do you make something which is infinitely dense and still can spin? The prediction is that the heart of a spinning black hole is not a singularity, but a ringularity. Love it. Did you come up with that term? I did not come up with that term, but I love it so much. I'm going to say it at every opportunity. Imagine a ring, literally like the kind of ring around your finger, and it's spinning. So it's a circle of infinite density, and it carries that angular momentum.

34:20And it can't collapse into a point like singularity because it can't get rid of its angular momentum. Okay, so we've talked about how you almost certainly have spin. And it feels to me like you'd almost certainly have charge because what is the probability that all the charges cancel out? And so we determined that a Schwarzschild black hole is probably less likely than a Kerr black hole. is a Kerr black hole also less likely than whatever black hole we're going to probably talk about that also has charge? Yes, absolutely. I think that most black holes in the universe probably have mass and spin and charge.

34:58And the effect of having charge is very similar to the effect of having spin. It changes where the event horizon is. So number one, if you have spin, you have a ringularity instead of a singularity. If you add charge, then you get a charged ringularity. It doesn't change the structure of the singularity because even a point could carry charge. Having charge doesn't determine the structure of the singularity. Sometimes y 'all do get naming right. Good job. But the spin and the charge do have a really interesting effect on the black hole. The spin forces it into a ringularity instead of singularity, but it also changes where the event horizon is.

35:37So as you speed up a black hole, you spin it faster and faster, the event horizon actually shrinks. Or as you add electric charge to the black hole, the event horizon actually shrinks, which creates a maximum spin or a maximum charge to a black hole. Because you can spin the black hole so fast, the event horizon shrinks to zero, and then boom, you get what's called a naked singularity, which we'll talk about a little bit more in a minute. A singularity that's not behind an event horizon. A singularity you could actually stare at, though. It would be rude. Please don't ogle our naked singularity.

36:13Wait, so could you escape from a naked singularity if there's no event horizon or am I misunderstanding event horizons? No, you're exactly correctly understanding the consequences of not having an event horizon. Absolutely. Wow, cool. The other fascinating thing about spinning black holes is they have much more complex space-time than people typically think about. You think about the space-time near a short-sized singularity, there's an event horizon, things fall in. That's the end of the story. But a spinning black hole has much more complex space-time. It doesn't just have an event horizon. It has another horizon within the black hole called a Cauchy horizon that we'll talk about later.

36:48And then outside the event horizon, there's a region called the ergosphere, where space itself is spun because the black hole is spinning. There's an effect in general relativity called frame dragging. So Einstein's general relativity is not just like Newton's gravity, but you're replacing the force with curvature. It predicts different stuff. So for example, a spinning object in Einstein's theory has different gravity than a non-spinning object. Whereas like Newton says, it doesn't matter. Like if the earth is spinning or not spinning, Newton predicts exactly the same force. Einstein says, no, no, that spin matters.

37:24It contributes to the gravitational energy and not in a simple way. You have an object near a spinning black hole, it will pick up a spin, right? So the curvature doesn't just pull things in, it can also spin things. We have these satellites around the Earth called Gravity Probe B, which measure these very small effects with incredible detail using these quartz balls that are the most spherical thing humanity has ever constructed. They have this incredible process where they create these things in Germany, and they send them to Argentina for this careful polishing, and they're incredibly spherical.

37:58And they're spinning in gyroscopes in space to measure the effect of the Earth's spin, the gravitational effect of the Earth's spin on these balls. Really an incredible experiment. I love that multiple nations were needed to make that happen. That's wonderful. I'm imagining some like old lady in Argentina with like a really smooth cloth and she's like rubbing it and rubbing it and rubbing it. And she's the best smoother in the world. So it had to go to Argentina. Exactly. You know, there are really bespoke processes like also for developing the massive lenses needed for telescopes. There's like a few people who like know how to do this and cook it just right.

38:33And like it's still an art. Anyway, outside the event horizon is the ergosphere. You can do cool stuff like drop stuff into the ergosphere, and it'll pick up a spin and then come back out. And so you can extract energy from the black hole this way. Oh, man. So if we were closer to a black hole, we could have free energy. Yeah, this is called the Penrose process. You're slowing down the spin of a black hole by stealing its spin. Absolutely. Something about that feels unsafe. life. Again, don't let Kelly drive. Nope, nope, nope. Or extract the energy from a black hole. But much more interesting than what's outside the black hole is, of course, is what's inside the black hole.

39:13Let's talk about a naked singularity. To me, this is one of the most tantalizing ideas in physics because seeing the singularity would tell us so much about the universe. We talked earlier, gravity tells us it should be a point or a ring. Quantum mechanics says, no, that's impossible. But doing those calculations is hard. People have tried it. They predict X. They predict Y. What's really there? If we could just see it, if the universe could just tell us what's going on, that would be such valuable insight and guide us in forming a deeper theory in physics and understanding the whole nature of reality and the universe.

39:46So seeing the singularity would be incredibly powerful. And when we come back, we're going to talk about how to take the clothes off a black hole so that you can see inside.

40:24We'll be right back. Must be 21 plus. Moto Casino. America's Social Casino. Make it a summer of life at Credit Union 1 Amphitheater. Get four lawn tickets for just$99 and see Evanescence on July 8th. John Mellencamp on July 11th. The Black Crows and Whiskey Myers on July 24th. Neo and Dacon on July 28th. Avenged Sevenfold and Good Charlotte on July 30th. and many more. Get your friends and grab tickets now at credituniononeamp.com. Hey, everyone. It's Cal Penn, host of Earsay, the Audible and iHeart Audiobook Club. This week on the podcast, I'm sitting down with Lily Chu, the author of the Audible original romantic comedy Just Kiss Already.

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41:57That's always fascinating to me. How they just bring in all these different nuances and really make it fun and interesting and distinctive. Listen to Earsay, the Audible and iHeart Audiobook Club on the iHeartRadio app or wherever you get your podcasts.

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43:29All right, Daniel, you and I are having a creepy afternoon talking about how to derobe a black hole. Let's talk some more about naked singularities. How can you see inside? Do you think it's inappropriate to like undress nature and try to understand how it works? I mean, I think animals are walking around naked all the time. We're very comfortable with it. It's the physicists that are uncomfortable. All right. That's fair. That's fair. So how do you take apart an event horizon? We always hear you can't see inside an event horizon. That's true for a short-sized black hole. But for a black hole that's spinning, where the event horizon is depends also on that spin and also on the electric charge.

44:06Remember that Einstein's gravity is more complicated than Newton's gravity. Newton's gravity just basically has charges and where they are. But Einstein has a stress-energy tensor, and different things contribute in different ways. Remember the episode where we talked about like why potatoes moving near the speed of light don't turn into black holes because they have a lot of energy. Well, that kinetic energy doesn't contribute the same way that the mass energy does, which is why potatoes don't turn into black holes at high speed. And so in the same way, like the spin of the black hole or its electric charge, they do contribute to the gravitational energy of the object, but not in the same way as just like adding mass to the black hole.

44:42So if you add spin to the black hole, you do change the gravity. But remember, like in the example of Gravity Probe B, it's complicated. And so what happens as you spin up the black hole is the event horizon actually shrinks. And is it harder to see because it's shrinking? No, we decided that that makes it so you can see it. It doesn't become harder to see. It's just now it's spinning. And some of these black holes in the universe we think are spinning super duper fast. So their event horizons are smaller than they would be otherwise. But if you could spin it beyond some threshold, then in principle, you would undress the black hole.

45:15Its event horizon would be at radius zero. And so if you wanted to try to spin it up so you could do that, could you throw a bunch of extra mass at it that was spinning the right way to make that happen? Yeah. So this is an area of much debate and confusion. General relativity in principle allows naked singularities, but it doesn't tell you how to make one. right and this is the problem with general relativity a lot of times it's like general relativity allows for wormholes like if one existed in the universe it wouldn't be breaking the rules but it doesn't tell you how to go from we don't have a wormhole to we have a wormhole it's like saying soufflés are possible okay but what's the recipe i don't know how to make that arrange the particles into a souffle like it's important distinction and so people have tried to go from like non-spinning black holes and think about adding electric charge or think about adding spin, like keep dropping stuff into the black hole and angle it away from the core so that when you're adding the mass, you're also adding spin, right?

46:11Spinning up the black hole, getting faster and faster. And so people have wondered about like, what happens when you reach the maximum spin? Is it possible in our universe to overspin a black hole and reveal the singularity inside of it? Roger Penrose has his cosmic censorship hypothesis. He just predicts like, no, it can't happen. There's something in the universe that's going to prevent them from existing. But remember, people also thought that about black holes in general. And then they were like, oh my gosh, these things are real? What? In 1991, Stephen Hawking bet John Preskill and Kip Thorne that these things are impossible.

46:47And this bet today still unsettled. Oh, I guess Hawking wouldn't pay up either way. Yeah, exactly. And so some people have done calculations, try to figure out like, well, what would happen if you tried to overspin a black hole? Like literally what would prevent you? And there's some calculations out there that suggest that it's impossible. That as you drop an object in, it loses angular momentum due to a back reaction. The acceleration of the object into the black hole causes gravitational emission, which effectively loses that angular momentum. So it's going to radiate away some angular momentum.

47:19Just the same way that if you accelerate an electron, the way that happens is by emitting photons. Like for an electron to turn left, it has to emit a photon right. And so the idea is if you drop stuff into a black hole in a way that would increase its spin too close to the maximum, it's going to radiate away some of that spin as gravitational waves. So if we can't make it spin faster, is there anything else that could make it spin faster? Or is this just something that can never happen because nothing's going to spin up a black hole? There's a lot of disagreements. And these calculations are hard.

47:52So nobody knows is the answer if this is possible or not. I would love to have a black hole and shoot a bunch of stuff into it and see what happens. We don't know. We just don't know. So maybe naked singularities are possible in the universe, or maybe these calculations are correct, and you just can't overspin or very similar argument for overcharging a black hole, that there's a maximum charge to a black hole. We just don't know. But that's a really fascinating kind of singularity and naked singularity. Okay. Okay. And so if I can take a step back for a second and do a big overview, basically, so we're talking about what's happening at the center of black holes, and the answers are either something completely different than everything we've talked about, because we get infinities, which means maybe we're wrong.

48:37Most likely outcome, yes. Okay. Or you can have a naked black hole, a Schwarzschild black hole, and a Kerr black hole, if those equations are correct, and it turns out we are describing something real. Okay. And if you have a black hole that has spin and charge, it's called a Kerr-Newman black hole. And there's another variation where there's a black hole that's not rotating, but it has charge, and that's called a Reisner-Nerdstrom black hole. So you have all the varieties there in general relativity. But those are all the classical predictions. They all ignore quantum mechanics. So we've talked about black holes that have charge, spin, and mass.

49:10Have we looked at every permutation of those three traits now? Yes, we talked about all those variations, but there's still other kinds of singularities that we can explore. Like even in those scenarios, we're assuming that the black hole is symmetric, that as the mass falls in, it's like a sphere. Because a star is mostly a sphere, right? But in the universe, nothing is ever perfectly a sphere. So there's another kind of singularity called a BKL singularity, after three physicists whose names start with BK and L, that describes the chaos you might get at the core of a black hole if it's not actually symmetric.

49:48Okay. Yeah, I guess, to be honest, I'm having a little trouble imagining. So when things spin, I always think of them as becoming more spherical. I'm having trouble imagining an asymmetrical black hole, but that is the limit of my imagination. So, okay, how would— Well, look at the sun. Is the sun perfectly spherical? It has features on the surface, which means that you can tell one location on the sun from another location. It's not perfectly spherical. And you might think, okay, those are small things. But the problem with gravity is it's very nonlinear. So small deviations create larger deviations.

50:19Like the whole reason we have structure in the universe is because gravity is nonlinear. And it started from very small deviations from perfectly smooth to make like stars and galaxies. And gravity is very powerful. another difference between Newtonian and Einsteinian gravity is that in Einstein gravity, the gravitational energy itself has gravity. And so think about what happens, for example, as things are collapsing. You get tidal forces, which we've talked about a lot, right? Things get stretched out and squeezed as you approach the singularity. But if you follow those calculations through, those tidal forces contribute also to the gravity.

50:56And so actually the tidal forces end up oscillating. So you get something which was compressed like in the long way, like a football, and then those tidal forces give a feedback effect, and now the thing gets squished and it gets compressed in another direction. So the point is, if you're not perfectly smooth, you're going to create all sorts of crazy chaotic fluctuations. Any tiny deviation from perfectly smooth symmetry is going to create chaos. So this collapse is not symmetric, but very chaotic. So that's the idea of a BKL singularity. It's this chaotic gravity. And we're not used to thinking about gravity as having fluctuations and randomness.

51:32This is still deterministic, but it's so hard to calculate because it's so sensitive to the initial conditions that we call it chaos. It's not random. It's chaotic. So that's what a BKL singularity is in broad terms. So you have made me switch from thinking, how could it not be a perfect sphere to how could it possibly be a perfect sphere? And that's probably the right way to think about it, right? Yeah, it's just much, much harder. And so in physics, what we do is we say, the universe is too complex to model completely. So let's take a simplified approach and get rid of some of the details we hope are irrelevant so we can get sort of the big picture view, which is why you start with spherical objects that are not spinning, have no charge, and you do that calculation.

52:15And then you're like, okay, I think we figured that out. Let's add this feature. Let's add that feature. And so we're trying to move more gradually towards a more realistic description of the universe. Okay, so if it's chaotic, then I imagine it's also inconsistent. If you look at it year to year, it probably has a slightly different shape. Would that be fair to say? Yeah, but we're talking about what's happening inside the black hole, so we can't see it. It probably also means that the event horizon has these kind of ripples too, right? Because the event horizon is determined by the curvature, but these effects might be subtle.

52:48And again, we've never directly measured the extent of the event horizon, but that could be super cool. see a fluctuating, oscillating event horizon. Another kind of singularity people talk about a lot is the Big Bang singularity. And this is another kind of singularity, but it's quite different from a black hole singularity. People really like to make these connections, be like, is our universe inside a black hole? Because black hole's a singularity and the Big Bang was a singularity, dot, dot, dot, we're inside a black hole. Awesome. Pop science points, right? But the singularity that might have existed at the beginning of the universe is a very different kind of singularity from the one that's at the heart of a black hole.

53:23It's a singularity not in space, right? A black hole singularity in principle should last forever and is at one location in space, right? The Big Bang singularity says the universe is old and cold. That's where we live now. But if you wind the clock back, things get hotter and denser, right? And so the universe was denser. And as you go back in time, things get denser and denser and denser. And eventually, you get a singularity in density at one moment in time, but everywhere in space. So black hole singularity, one point in space, everywhere in time. Big Bang singularity, everywhere in space, one moment in time.

54:02So technically a singularity in the same sense of singularities as having infinities, but physically very, very different from a black hole singularity. Was it spinning? we don't know that would be the whole universe spinning right and we think probably the whole universe on average has been zero but that's a whole other fascinating topic and also remember that this prediction that the universe goes to a singularity and density that also ignores quantum mechanics what really happens is you go back to a certain moment 13.8 billion years ago and beyond that we can't predict with just gravity we need to incorporate quantum mechanics and we don't know how to do that.

54:39So modern theories of the Big Bang do not include a singularity. They have a question mark before this moment when things are so dense we can no longer calculate. But there is a concept of a singularity, which again ignores quantum mechanics if you want to go that far, but it's different from a black hole singularity. This moment beyond which you can no longer calculate without knowing how to do quantum gravity, sometimes called the Planck temperature, like when things get so hot, we can no longer ignore gravity. Or my favorite description of it is absolute hot. You've heard absolute zero, like the universe can't get below zero.

55:11This is absolute hot. It's like the hottest possible temperature beyond which like temperature doesn't make sense anymore. Like we don't know it can't get hotter. We just, we don't know anything about what happens beyond the Planck scale. Do we know what temperature is absolute hot? Yeah. It's the Planck temperature. It's a very big number. Oh, okay. But it's, it's not like 5 ,000. It's just some very big number. Got it. Okay. All right. So let's talk about the last two kinds of singularities that Julie mentioned. These are in-flying and outgoing singularities. These are not standard terms for singularities.

55:44You don't find them often in the literature in general relativity. These are phrases made up by Kip Thorne and explained in his book, The Physics of Interstellar. Kip Thorne definitely knows a lot of general relativity, a lot more than I do. Dude is a total expert and a badass and a Nobel Prize winner for general relativity. So no criticism implied in any of these comments. It's just like he's very poetic with his words and not all those words have caught on everywhere. So if you Google this stuff, you don't find like textbooks on it. But the dude knows what he's talking about. When he refers to an in-flying singularity, he's talking about the complex space-time structure inside a spinning or charged black hole.

56:23So remember, this black hole is not just a sphere of mass that's gotten compressed into a point, it's spinning. And so the space-time is much more complicated on the outside and on the inside. So there's the event horizon, but if you go past the event horizon, there's another horizon. It's called the Kaoshi horizon. So again, these space times have more structure than just an event horizon and a singularity. There's this Kaoshi horizon. Outside the Kaoshi horizon, you can actually survive. You can live. People have theories that you could have stable orbits within the black hole, and maybe even life could evolve, which could be amazing.

56:58Within the Cauchy horizon, things get crazy. The Cauchy horizon essentially is the point where classical determinism breaks down, where there's not enough information to predict what's going to happen in the future. Remember that the equations of general relativity are nonlinear, which means they blow up. Sometimes small deviations in your initial conditions can lead to very large differences in your predictions, right? You're going from infinitesimal changes in your conditions to huge predictions in the future, that's also a kind of infinity. And so this is what Kip Thorne means by singularity here.

57:34Okay. And so just to confirm, it sounds like what you're saying is this is the kind of singularity where we don't understand it at all as physicists. And so when you say there's not enough information to predict the future, that's not like people living in the Couchy horizon can't predict the future. It's us. We can't predict what happens in that situation. We can't predict it with our limited understanding of relativity and general relativity and our current ability to do calculations. It doesn't mean that it's impossible. Okay. Got it. And so in that sense, is this a physical thing? Does it reflect the limit in our theory?

58:09There are some interesting physical effects here, like in falling radiation or matter, blue shifts very dramatically as it approaches the Cauchy horizon. And so the energy density diverges. You get these predictions of essentially infinite energy density, which don't seem to make sense. And so this is what he means by the in-flying singularity. There's this other threshold. After you come into the black hole, as you fall in towards the ringularity, you experience this in-flying singularity of the Cauchy horizon. Okay. But what if you were trying to get out? Because it sounds like you don't really want to be at the middle of a black hole.

58:45So what is an outgoing singularity? And outgoing singularity is related to the topic we talked about earlier, the BKL singularities. You have a collapse of black hole that's not symmetric, right? Or maybe you have like two black holes that collide. And so that's very much not symmetric. You have an axis along which they collide. So again, the non-linearity of the Einstein equations lead to chaotic effects, and you can get things like propagation of a curvature shockwave that's moving out from the core. So you can get this outgoing singularity. What we mean there, again, is a singularity in the curvature.

59:18So like huge gradients, very nonlinear reactions, not a dot of matter that's infinitely dense, but a deviation in the curvature that's moving in space and time. Okay. And this is maybe not the most important question that I could be asking right now, but you said this was in a book called The Physics of Interstellar. Are these concepts part of that movie, which I have to admit I've never seen? You have not seen Interstellar? Wow. Wow. No, I know. Wow. And married to a nerd, never seen that movie. He's never seen it. I know. Oh my gosh. Is that on purpose? You guys like boycotting that movie? No, just never got around to it.

59:54Maybe I need to. Well, there's lots of fascinating and wonderful stuff about that movie. There's also stuff I can't stand about that movie. So anyway, it's a very popular movie and a lot of real physics went into it. Not all the plot elements are based in sound physics, but a lot of it is. And so Kip wrote this book, The Physics of Interstellar, for people who are interested diving more deeply into these topics. So some of the stuff in the book, The Physics of Interstellar, is not covered in the movie. So we don't have in-flying or outgoing singularities in the movie, as far as I can recall. Okay, got it.

1:00:25All right, so that's our tour of singularities. We think that the appearance of these singularities in our predictions is a sign that those predictions are probably nonsense. sense, well, we don't really know because sometimes the universe acts sort of nonsensical in a way that seems crazy to us, but later we come to learn actually makes more sense than anything we could have imagined. And so we always should be ready for surprises. And as usual, there's a lot more interesting, rich physics here that goes well beyond what you typically see in pop-sci coverage. And thank you so much to Julie for inspiring this rousing conversation about the many kinds of singularities.

1:01:00Let's check in with Julie to see if we scratched her singular itch. Consider my singular itch scratched, or maybe my ringular itch? I did not know regularities were a thing. I like how you describe singularities as a warning sign from the math and an indication that something is wrong, like the math and the physics contradict each other, but also we can't say for sure. So if you physicists could figure out quantum gravity for the rest of us, that'd be great. You also inspired new questions to ponder, like if there are fuzzballs instead of black holes, or if life could evolve inside a spinning or charged black hole.

1:01:36Wild. And yep, I absolutely did read The Science of Interstellar by Kip Thorne, which is where I got those terms, so it was helpful to have that terminology cleared up. Thanks again. All right, thank you very much, everybody, for tuning in to this survey of several singularities. We hope this helps stretch your mind to the limits of what humans can conceive of. Until next time!

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