The several styles of singularities

00:00:07
Speaker 1: Few words are as heavily loaded as the word singularity. To AI futurists, it means the moment that ais can teach themselves and might accelerate beyond human control. To physicists, it means a divergence, a divide by zero, a point of nonsense, a failure, a breakdown. To the broader public, it represents a mystery, an unseen, unknown point at the heart of black holes, something fascinating and mind bending, something we are a little bit afraid of, but also entrance by a bizarre extremum that might reveal something deep about the nature of the universe. To you, our listeners, it means a whole episode dedicated to demystifying, detoxifying, deconstructing the several subclasses of singularities. So welcome to Daniel and Kelly's Extraordinary Singular Universe.

00:01:10
Speaker 2: Hello. I'm Kelly Wienersmith. I studied parasites and space, and I'm excited to talk about singularities today.

00:01:15
Speaker 1: Hi, I'm Daniel Whitson. I'm a particle physicist, but I'm actually not a singularity. There are other Daniel Whitson's. How many, I'm not sure I've only ever found one he's an artist in the UK and he's quite good, if I have to say so myself.

00:01:30
Speaker 2: Oh fantastic. It's something in the name. Maybe. I don't think there's any other Kelly Wienersmith, which is why we picked this name. Have I told you the story about how I ended up with this name?

00:01:41
Speaker 1: No, tell us the story, all right.

00:01:43
Speaker 2: So I was working on my master's degree and I published my first paper on smallmouth bass, and there's a lot of papers on smallmouth bass, and so I looked to see how hard was it going to be for people to find my first paper by looking up papers by Kay Smith, and there were literally like over one hundred thousand, and if you did k L Smith, there was like, you know, eighty thousand or there were still so many that it was going to be really hard to find me, Okay. And then I fell in love with Zach, and I was like, all right, I don't really want the last name Wiener. But with the order.

00:02:19
Speaker 1: You're telling this story makes it sound like you picked Zach because he had an unusual last name. No.

00:02:24
Speaker 2: No, So you know, I dated some guys with some pretty great last names.

00:02:28
Speaker 1: Wow.

00:02:29
Speaker 2: And then there was Zach, who I fell in love with.

00:02:34
Speaker 1: And despite the last name I see.

00:02:38
Speaker 2: So I looked up how many papers there were by K. Wiener and K. L Weener and they were literally still thousands.

00:02:46
Speaker 1: Wow.

00:02:46
Speaker 2: And I was like, I don't really know if I want to take this name if it only helps me by like one order of magnitude. And so we smoothed our names together and we our little family are the only Wiener Smith's I found. There's a Wiener hyphen Smith who's an obstetrician, which is amazing because she's helping people Smith Wieners, which I love and.

00:03:08
Speaker 1: Uh, professionally accurate last names. I love it.

00:03:15
Speaker 2: That's right. But now Google scholar Kelly Wiener Smith, you only get me. All right, we've gotten off track. I am a singularity.

00:03:23
Speaker 1: You are the one and only. Congratulations.

00:03:26
Speaker 2: Oh thanks. I don't think there's a lot of vying for this position.

00:03:31
Speaker 1: And Kelly, if you were a point particle, then there would be an infinite density if Kelly Wiener Smith's at you.

00:03:37
Speaker 2: There are days where it feels like that's happening as we cruise onto the holiday season, and that is.

00:03:46
Speaker 1: Exactly what we're talking about here today. You're listening to this episode in January, after surviving the holiday season, potentially gaining mass, potentially losing mass, however you do it. But today we're talking about that very massive question of gravitational singularity.

00:04:00
Speaker 2: Amazing, and whenever we have a massive topic to handle, we always go to the extraordinaries to see what they think we do.

00:04:07
Speaker 1: This question actually was inspired by an extraordinary he wrote to me. Julie Bud wants to learn more about singularities. Here's her question.

00:04:16
Speaker 3: Hi, Daniel and Kelly, I'd love it if you could do an episode about all things singularities. I have this misconception, which I think maybe a common one, of a singularity just being a tiny point in space where density becomes infinite. But I recently learned it's actually kind of just a term for where our understanding of physics breaks down and we don't really know what happens. I also learned that there are different types of singularities inside black holes, like infalling and outflying singularities, and a BKL singularity, which I can almost wrap my head around but also not really. So I'd love if you could do a deep dive into what singularities are and the different types of them.

00:04:56
Speaker 2: Thanks, fantastic question from Julie. Frankly, I don't know the answer here, so I think I'm going to learn a lot today.

00:05:01
Speaker 1: And I love this kind of question because one of the things I love doing on the podcast is going deeper than your typical pop side treatment, breaking through to the next layer of knowledge, and really sharing with people a lot of the subtlety and the nuance and how people on the forefront of knowledge are actually thinking about this stuff.

00:05:19
Speaker 2: Yeah, and before we get to how the scientists at the forefront of knowledge you're thinking about this stuff, let's see how the people on the street are thinking about this kind of stuff.

00:05:28
Speaker 1: So I went out there and asked folks, what is the best kind of gravitational singularity. Here's what people had to say.

00:05:36
Speaker 4: Gravitational singularities weren't real, so maybe the best one is one you can study in your particle collider kind it would make me lose ten pounds. I like classical gravitational singularity is the best because I don't like the idea of space being broken up into pieces.

00:05:51
Speaker 1: As far as I can tell, it's being a grandparent, the kind that's close enough to provide insight into the universe and far enough away that I don't have to worry wry about her breaking my stuff.

00:06:01
Speaker 4: I would say a black hole a naked singularity, because you could observe it and learn from it.

00:06:08
Speaker 1: I have always had a fond spot for neutron stars. Black holes are the best kind of gravitational singularity, the singularity where it all started with the Big Bang, The one that lets you view itself from afar, doesn't spaghetify you and tells you all it's secrets. The one that doesn't have any side effects.

00:06:28
Speaker 4: All the singularities, all the singularities, all the singularities. Some cosmic grads up being the telescope. It looks like there's a ring on it. That's the accretion disking. Gravity is lensing it. We'd like to study quantum gravity inside of it, but if we visited, we just s begetify in it will uh oh.

00:06:45
Speaker 1: The kind that stays the heck away from me.

00:06:47
Speaker 3: Is a black hole or neutron star.

00:06:50
Speaker 2: Well, I think from now on the rule is that everybody has to sing their answer to the tune of a Beyonce song.

00:06:57
Speaker 1: Wow, dude, really raise the bar for everybody, didn't he?

00:07:01
Speaker 2: Thank you? Zach?

00:07:04
Speaker 1: All right, So let's be singular in our focus and talk about what singularities are. And I want to start by talking about singularities sort of mathematically and theoretically, because like many things in science, this word is overused.

00:07:19
Speaker 2: I think these days I hear about it most and as it relates to tech. But we are not at all talking about tech singularities today.

00:07:26
Speaker 1: We are not talking about that moment when ais can teach themselves and accelerate beyond human control, and whether that's already happened or not. We're talking about singularities from a mathematical and physical point of view, and unfortunately, there's not a whole lot of agreement on what singularities mean. There's sort of two different kinds of singularities, though there are ways to unify them in your mind. The first one is essentially what Julie mentioned, which is where there's a breakdown in your theory because you predict something unphysical and infinite. Like if I flip a coin and I want to calculate the probability for the coin to come up heads, and my answer gives me infinity, I'm like, well, that can't be right. The probability has to be less than one so infinity is wrong. Something went wrong in my theory I divided by zero, or I just made a dumb error, or the theory is broken. Right, that's an unphysical prediction, something which can't happen. It's outside the bounds. And that happens a lot when math confronts physics. Right, mathematics, let's you do lots of things which the physical world doesn't let you do. A simple example of that is like when you throw a ball, it follows a parabola. That parabla moves forward, but also it could move backwards in time, and the same solution allows the ball to like go deep into the earth behind you or whatever. Obviously, that's not going to happen. There's a boundary there that you haven't included in your calculations. But there's lots of times when you're solving problems in math and there's an unphysical solution that you don't consider. And so one idea of a singularity is when your math predicts infinity but physics rejects that.

00:08:57
Speaker 2: I guess I hadn't thought of singularity as another word for were we're probably wrong about this, but is that the right way to think about it?

00:09:04
Speaker 1: It's an indication that something is probably wrong with your theory. Not all the time. It could be that the infinities are real. We don't really know. But if your physics is telling you that the infinities are impossible and the mathematics is predicting infinity, then there is something wrong with your theory. That's the idea, okay, and it doesn't have to be gravitational. You can take, for example, an electron and think about the electric field of the electron. How does that electric field vary with distance from the electron? Well, it goes like one over distance square, like most things in physics. So you twice as far away, the electric field drops by a factor of four. Well, what happens if you get twice as close. The electric field goes up by a factor of four. What if you get twice as close again, up by another factor of four. If the electron is a point particle, you can get infinitely close to it. What is the electric field at the electron itself? Well, you're dividing by zero or it's approaching infinity, And so the electric field in classical electrodynamics is predicted to go to infinity at the electron itself. There's a divergence there, a singularity and infinity. We don't believe the electric field really is infinity there. This is a breakdown of the theory because the electron is not really a point particle. There's a limit to how close you can get to it. So that's an example of like, you didn't build all the physics into your theory, and then you took the theory who literally and extrapolated it beyond where you thought it was relevant, and so you got a singularity. It's a warning sign from the mathematics to say, oh there, buddy, back up and think about what you're doing.

00:10:30
Speaker 2: Interesting, So when you get a singularity like that, how much of the theory do you throw away or do you just say this theory is good up until this point where we don't understand something.

00:10:41
Speaker 1: Yeah, exactly, you can just put a boundary and say, well, this theory works up to here, beyond that it's not applicable. And that's the case where basically every theory of physics we have right, every theory has boundaries because they start from some assumptions, and those assumptions are only true in limited cases. Even like the standard model of part of physics are best. Quantum theory that predicts things to ten decimal places. We know it's not valid everywhere because in order to do any calculations we have to ignore gravity. And a lot of times you can ignore gravity. When two particles interact to the Large Hadron Collider, Gravity's are relevant, but it's there, and if those particles get really really massive, it's no longer irrelevant. So when things get really really massive, we're really really dense, then you can no longer ignore gravity, and you can't just calculate blindly assuming gravity doesn't exist. So they're always boundaries to your theory. And when principle, you'd love to find a new theory that doesn't have those boundaries, or works beyond the boundary or something. But there's lots of different possible approaches.

00:11:39
Speaker 2: And I seem to remember infinities coming up in our understanding of gravity when we were talking with Jonathan Oppenheim and Thomas van reet Am. I remembering that correctly.

00:11:48
Speaker 1: Yeah, exactly. String theory is an extension of these theories that avoids some of the infinities that appear in the standard model and in gravity. So it's an example of a quantum gravity theory that avoids some of those infinities by replacing points with lines. Essentially, instead of having dots, you have strings. And of course it's still very controversial, but that's an example of how you might extend a theory to be more broadly applicable. Or you could just say, look, this theory works here, and we have a different theory over there. That's what we do. For like water, we have a theory for fluids, and we have a different theory for crystals and different theory for vapor And we don't say we want a general theory of water, you know, we're like, look, Navria Stokes works here, and crystal theory works there, and we're fine. And so there's lots of different approaches, and so a singularity more generally is where things go to infinity. And in the case of gravity, for example, you have gravitational curvature in the heart of the black hole. We'll talk about that more in a minute. That goes to infinity. And that's a question is does that really happen or is it a sign that the theory is broken somehow? Or in the early universe, the Big Bang was a singularity, and in the future if there's a big crunch that could be a.

00:12:57
Speaker 2: Singularity, don't I don't want there to be a big crunch, Daniel, what.

00:13:02
Speaker 1: You want doesn't really matter, unfortunately, Kelly.

00:13:04
Speaker 2: Yeah, that's a little harsh. But also because we're extrapolating an infinity, I'm going to decide that physicists are probably just wrong about that.

00:13:13
Speaker 1: Okay, great, I hope that works for you. That's one concept of a singularity, where things get infinite as sign that probably your theory is breaking down. There are other concepts of a singularity. One that I think is really fascinating are paths that are not extendable. So imagine you are moving through space. You can go here, you can go there. There's always a place you can go right, you can walk around, you can go downstairs, you can go upstairs, you can take off from the Earth, you can go to Mars, whatever. There's always somewhere to go. So your path is infinitely extendable. But what if there was a place where a path couldn't continue, where like it just ran into a dead end, like a boundary or an endpoint. A great example of this is the heart of a black hole. Inside a black hole, space is curved and there's only one direction of space. It just goes towards the center. And so your path will continue towards the heart of the black hole, and that's it. It just ends there. You'll be there forever at the heart of the black hole. So that path is not extendable. And so that's another way to think about a singularity. It doesn't have to be in conflict, but it starts from a different definition and so sort of leads you in a different direction conceptionally.

00:14:22
Speaker 2: So like, how generalizable is that use of the word singularity? Like I get lost when I'm driving all the time. So when I go down a wrong road and I hit a dead end, can I turn around to my passengers and be like singularity or is that? Is that the incorrect usage of this word.

00:14:39
Speaker 1: Yeah, you can't blame math for the reason you get lost, Kelly. Sorry, Unfortunately, you know math is not that useful. It needs to really be a non extendable path, you know, partner space where you just cannot continue.

00:14:55
Speaker 2: All right, So you hinted that we're going to get into black holes again, which I think is maybe one of the top topics that the extraordinaries ask us about. Nobody ever gets tired of hearing about black holes. So tell me about a black hole singularity. No, wait, first, remind me what a black hole is.

00:15:11
Speaker 1: Yeah, So to understand what a black hole singularity is, we have to remind ourselves how black holes work. And remember that black holes have very powerful gravity, so powerful that not even light can escape. They have an event horizon beyond which nothing can return. But you need to unshackle yourself from you intuitive sense of like Newtonian gravity, where gravity is pulling on stuff, where black holes are like huge vacuum cleaners sucking on things because force. It's not the right way to think about gravity, because gravity is not a force and also doesn't work for black holes. Like black holes, we know can bend the path of light and can trap light, but light has no mass. And then Newtonian gravity the gravitational forces between two objects with mass, and so photons shouldn't feel black holes in Newtonian gravity, but they do in the universe, so we know Newtonian gravity is wrong. Actually had a list are writing last week to correct me and say, actually, photons do have mass. We know that because they feel gravity because they get sucked into black holes. And it was like, interesting argument. Let's unwind this to see where you went wrong.

00:16:12
Speaker 2: Anyway, And I remember that email. They titled it a massive correction. Yeah, that was great.

00:16:20
Speaker 1: They definitely had a lot of gravitas in their email. I welcome it. Please if you think I made a mistake, right to me, I'm pretty sure I'm right on this one that photons do not have mass. And the right way to think about black holes is not in terms of a force, but in terms of the curvature of space. Right, So, mass bends space, which means it changes the relationships between objects their distances. This kind of gravitational curvature is very tricky to think about. I think about it in terms of relative distances between pairs of objects. And if you like throw a bunch of ping pong balls into space, and then you measure all the distances between those ping pong balls, and you're like, this one is for me to from that one, this one is six meters from that one. Then you have all these like pair wise distances. You have all your ping pong balls, and you know the distances between all of them. Right now, the way to think about curvature is to think about could you actually like put meter sticks between all of those ping pong balls and have it all line up. If you can, then space is flat. You've measured those spaces and you have those meter sticks, and everything sort of cooks together. But if you can't, if you can't do that with like straight meter sticks, then it's because the relationships between the points have become distorted. Because space is curved. You can't see the curvature of space directly, but you can measure it by like putting stuff in space and measuring the distances between them and see, like do they click together? Can I describe that without gravitational curvature?

00:17:46
Speaker 2: Okay, to be honest, I always have trouble with this idea of space being curved. But would it be similar to say, like, all right, so an object isn't going into a black hole because a black hole is pulling it in. It's going into a black because space is curved in such a way that it's directing it into the black hole. And that that's a little bit different.

00:18:06
Speaker 1: Yes, So now we're talking about the consequences of the curvature. So if you have the idea of a curvature in your head, now what happens to stuff?

00:18:12
Speaker 3: Now?

00:18:12
Speaker 1: The space is curved. Is that the concept of like moving in a straight line is different. Your intuition about a straight line assumes flat space. You're like, I'm going to go from here to there. I'm just going to go from here to there straight line, a shine of flashlight. It's going to go from here to there in a straight line. But what is a straight line in curved space is following the curvature of space itself. And so if you just have an object in free fall, it's moving under the influence only of the curvature of space. It's going to follow the curvature of space. And so if space is flat, it's just going to drift the way you would normally into it. But if it isn't, then it's going to bend. It's going to follow that invisible curvature of space. And so the Earth goes around the Sun because it's following that curvature, and things fall into the black hole. Yes, Kelly, because they're following that curvature of space.

00:18:58
Speaker 2: And it does gravity make that curvature or these two different things.

00:19:02
Speaker 1: So gravity sort of is that curvature. Right. Gravity is not a force, it's just the effect of that curvature. We can't see the curvature, but we see the curvature's effect on stuff, and we call that gravity. And we know it's not a force because like when you jump off a building, you are feeling no force, no acceleration. You're moving towards the center of the Earth. We say, under the influence of gravity. But if you like held up a scale underneath you, you would feel no acceleration. There's no force happening to you there. It's not like a chemical rocket. If you fire a chemical rocket, then you definitely feel that acceleration. Right, If you like hit the brakes in your car, that's acceleration you feel. Those Those are real forces. Gravity is not a real force because it doesn't create those feelings of acceleration. You're just naturally following the curvature of space, which means something amazing. If you're falling into a black hole, you don't feel any gravity, but you're dying, especially if you let Kelly do the driving.

00:19:58
Speaker 2: Oh all right, all right, you know what, I need some time to recover from that insult. So let's take a break and when we get back we'll talk more about this concept of black hole singularities. All right, I've recovered from the wicked burn Daniel gave me regarding my driving skills.

00:20:32
Speaker 1: You're the one who said you're driv into singularities.

00:20:35
Speaker 2: I said, well, mate, what happened to?

00:20:37
Speaker 3: Yeah?

00:20:37
Speaker 2: Maybe I did? All right, you got me? All right, tell me about black hole singularities. Let's stop talking about my driving record.

00:20:42
Speaker 1: 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 life becomes trapped inside that curvature because the direction of space is just one d inside that black hole. Beyond 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 curvature of space itself becomes infinite. So like, what does that mean? Well, if you have two points in 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.

00:21:28
Speaker 2: So is this a case where the equations are breaking down or is this like actually what we expect will happen.

00:21:35
Speaker 1: 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. We'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 or gravity when you're doing quantum mechanical calculations on individual particles. But when you're talking about super tiny, dense objects like the heart of a black hole, quantum mechanics matters. Again. Quantum mechanics says that that prediction is wrong. It can't happen. You can't have that much mass isolated with that much energy in that small space. It violates the Heisenberg and certainty principle. It definitely would not happen. So what you've done here is take in general relativity, ignore quantum mechanics, but done it in a region where quant 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. 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, and so it's sort of a question mark.

00:22:47
Speaker 2: Is this level of nuance conveyed in like pop culture treatments of black holes?

00:22:53
Speaker 1: Or is it?

00:22:54
Speaker 2: How is this usually conveyed in pop science?

00:22:57
Speaker 1: Most of the popular science treatments just say that there's a single already at the hearts 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. So doesn't mean you shouldn't make those predictions and use them again, like as a diagnostic. But I think some of that nuance is missing, Yeah.

00:23:19
Speaker 2: Okay, 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.

00:23:26
Speaker 1: 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, is there a singularity? And it's hard, but do black holes exist at all? For a long time, they were just like a curiosity of the math, and people are like, well, this is definitely a sign that something is wrong and the universe would never let this happen. But 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 in the hearts of galaxies, We see them where stars have colapsed. Do we know that these are actually black holes that have an event horizon and potentially singularity within them?

00:24:06
Speaker 4: Not.

00:24:06
Speaker 1: Technically, we have only indirect evidence that these things are black holes, in 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 dwarfs, they can't be anything else in our physics. So the only thing left in the box is a black hole. But you know, 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.

00:24:42
Speaker 2: Yeah, and I really enjoyed our recent conversation about Bechdel stars and black holes are confusing, but we're we're learning more all the time.

00:24:49
Speaker 1: Yeah, and that's not a criticism of astronomers, like it's amazing what they've found. And you know, seeing black holes is hard. And even the event horizon telescope, which just image the accretion disk around the black holes, tells us a lot, but isn't direct observation of the event horizon itself. Right.

00:25:04
Speaker 2: Okay, so we've talked about black hole singularities, right, are there other kinds of gravitational singularities to talk about?

00:25:12
Speaker 1: Well, all the singularities we're going to talk about which makes me think of Beyonce. The singularity are at the hearts of various kinds of black holes, okay, and so less catalog those the sort of vanilla singularity, and the classic one is at the heart of a black hole that's very simple. It's spherical, it has a lot of mass, it 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 use a short style black hole, just a really massive stuff with no spin and no electric charge, then you get an event horizon that's spherically symmetric, and at its heart is that point that's singularity, the location of infinite density or infinite curvature, and that's the sort of the nilla classic singularity. I think most people think about when they think about black holes and singularities.

00:26:21
Speaker 2: 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.

00:26:29
Speaker 1: Yeah, exactly. And these characteristics of the black hole determine what's happening and ats the core. So if you just think about it, a lot of stuff, a star collapsing into a very dense object, that's a short style black hole. And that was the first solution to Einstein's equations ever found to describe a black hole. No spin, no charge, just mass.

00:26:47
Speaker 3: All right.

00:26:47
Speaker 2: 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 swar style, if I could say it, we've got the first kind of black hole we talked about what what? Okay, so we're going to be looking at variations on mass, spin, in charge. Our next kind has what spin?

00:27:08
Speaker 1: Right, It's very unlikely that something collapses into a black hole and isn't spinning. Why because everything in the universe is spinning. All 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 underd densities. With 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 fifty percent heads? Now you get a little bit extra tail sometimes or a little bit extra heads another time. To 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, Well, 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 schwartzy black holes. They're curve black holes. They have mass and.

00:28:31
Speaker 2: Spin, and so they're called curve black holes.

00:28:34
Speaker 1: curR kerr from the New Zealand physicists who came up with them.

00:28:38
Speaker 2: Ah, all right, curve black holes. Okay, so you wrote ringularity. What does ringularity mean?

00:28:44
Speaker 1: 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. Oh 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 at the heart of a spinning black hole is not a singularity but a ring gularity.

00:29:13
Speaker 2: Love it? Did you cop with that term?

00:29:14
Speaker 1: I did not come up with that term, but I love it so much I'm gonna say that at every opportunity, imagine a ring like 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 and it can't collapse into a point like singularity because it can't get rid of its angular momentum.

00:29:32
Speaker 2: 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 schwarz Child black hole is probably less likely than a cur black hole. Is a curb black hole also less likely than whatever black hole we're gonna probably talk about that also has charge.

00:29:59
Speaker 1: Yes, I think that most black holes in the universe probably have mass and spin and charge. And 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.

00:30:28
Speaker 2: Sometimes you all do get naming right, good job.

00:30:33
Speaker 1: But the spin and the charge do have a really interesting effect on the black hole. The spin forces it into aringularity instead of singularity, but it also changes where the event horizon is. So 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 you talk about a little bit more in a minute, a singularity that's not behind an event horizon, a singularity you could actually like stare at, though it would be rude. Please don't ogle our naked singularity.

00:31:20
Speaker 2: Wait, could you escape from a naked singularity if there's no event horizon or my misunderstanding event horizons.

00:31:26
Speaker 1: No, you're exactly correctly understanding the consequences of not having an event horizon. Absolutely.

00:31:31
Speaker 2: Whow cool.

00:31:32
Speaker 1: The other fascinating thing about spinning black holes is to 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 Cauchhi horizon that we'll talk about later. And then outside the event horizon there's a region called the ergosphere where 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. It contributes to the gravitational energy, and not in a simple way. You have an object near 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 pro b which measured 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, they send them to our Gentina for this careful polishing and they're like incredibly spherical and they're spinning in gyroscopes in space to measure the effect of the Earth's spin, the gravitational effect of the Earth spin on these walls. Really an incredible experiment.

00:33:13
Speaker 2: I love that multiple nations were needed to make that happen. That's wonderful.

00:33:19
Speaker 1: I'm imagining some like old lady in Argentina with like a really smooth cloth and she's like rubbing it and rubbing it, rubbing.

00:33:25
Speaker 2: It, and she's the best smoother in the world. So it had to go to Argentina exactly.

00:33:30
Speaker 1: 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, and like it's still an art anyway. Outside the event horizon is the ergosphere and you can do cool stuff like drop stuff into the ergosphere and you'll pick up a spin and then come back out, and so you can extract energy from the black hole this way.

00:33:53
Speaker 2: Oh oh man, So if we were closer to a black hole, we could have like free energy.

00:33:58
Speaker 1: Yeah, this is called the Penrose process, like slowing down the spin of a black hole by stealing its spin.

00:34:03
Speaker 2: Absolutely, something about that feels unsafe.

00:34:09
Speaker 1: Again, don't let Kelly drive.

00:34:11
Speaker 2: Nope, nope, nope, or extracts the energy from a black hole.

00:34:15
Speaker 1: But much more interesting than what's outside the black holes, of course, is what's inside the black hole. Let's talk about a naked singularity. To me, this is like one of the most tantilizing ideas in physics because seeing the singularity would tell us so much about the universe. Right we talked earlier, like 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 why. 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, so seeing the singularity would be incredibly powerful.

00:34:56
Speaker 2: And when we come back, we're going to talk about how to take the clothes off a black hole so that you can and see inside. All right, Daniel, you and I are having a creepy afternoon talking about how to de robe a black hole. Let's talk some more about naked singularities. How can you see inside?

00:35:29
Speaker 1: Do you think it's inappropriate to like undress nature and try to understand how it works?

00:35:33
Speaker 2: 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.

00:35:40
Speaker 1: All right, that's fair, that's fair. So how do you take a part in event horizon? We always hear you can't see inside an event horizon. That's true for a schwartziled 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. Remember 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 it's electric charge, they do contribute to the gravitational energy of the object, but not in the same way. It's just like adding mass to the black hole. So if you add spin to the black hole, you do change the gravity. But remember, like an example of gravity pro b it's complicated. And so what happens as you spin up the black hole is the event horizon actually shrinks.

00:36:46
Speaker 2: And is it harder to see because it's shrinking. No, we decided that that makes it so you can see it.

00:36:52
Speaker 1: It doesn't become harder to seeze 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. Its event horizon would be at radius zero, and.

00:37:10
Speaker 2: 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.

00:37:18
Speaker 1: 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? Do we have a wormhole? It's like saying slew flays are possible, Okay, but what's the recipe. I don't know how to make that arrange the particles into a southflay, 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. That when you're adding the master, you're also adding spin, right, spinning 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 nineteen ninety one, Stephen Hawking bet John Preskill and Kip Thorn that these things are impossible, and this bet today still unsettled.

00:38:41
Speaker 2: Ah, I guess Hawking wouldn't pay up either way.

00:38:44
Speaker 1: Yeah, exactly. And so some people have done calculations try to figure out like, well, what happened 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, just the same way that like 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.

00:39:31
Speaker 2: 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.

00:39:41
Speaker 1: There's a lot of disagreements, and these calculations are hard, so 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, of course, Okay, we just don't know. So maybe naked singularities are possible in the universe, or maybe these voculations 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.

00:40:13
Speaker 2: 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.

00:40:28
Speaker 1: Most likely outcome yes okay, Or.

00:40:30
Speaker 2: You can have a naked black hole, a schwarz Child black hole, and a cur black hole if those equations are correct, and it turns out we are describing something real, okay.

00:40:40
Speaker 1: And if you have a black hole that has spin and charge is called Akur 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 reister Nerdstrum black hole. So you have all the varieties there in general relativity. But those are all the classical predictions all ignore quantum mechanics.

00:40:58
Speaker 2: So we've talked about black holes that have charge, spin, and mass. Have we looked at every permutation of those three traits?

00:41:06
Speaker 1: 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 the 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 name 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.

00:41:40
Speaker 2: Okay, yeah, I guess to be honest, I'm having a little trouble imagined. 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.

00:41:52
Speaker 1: 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, and it's not perfectly spherical. And you might think, okay, those are small things, but the problem with gravity is it's very non linear, so small deviations create larger deviations. Like 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 new Tony and Einsteini and 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 title 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 title forces contribute also to the gravity, and so actually the title forces end up oscillating. So you get something which was compressed like in the long way, like a football, Then those title 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 just like chaotic gravity, and we're not used to thinking about gravity as like having fluctuations and randomness. This 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.

00:43:36
Speaker 2: 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? So that and that's probably the right way to think about it, right.

00:43:49
Speaker 1: Yeah, it's just much much harder. And so you know, 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. We can get sort of the big picture view, which is why you start with like spherical objects that are not spinning and have no charge, and you do that calculation and 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.

00:44:16
Speaker 2: Okay, so if it's chaotic, then I imagine it's also like inconsistent, Like if you look at it, you know, year to year, it probably has a slightly different shape. Wouldn't that be fair to say?

00:44:26
Speaker 1: 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. And again, we've never directly measured the extent of the event horizon, but that could be super cool. See a fluctuating, oscillating event horizon.

00:44:47
Speaker 2: Yeah.

00:44:47
Speaker 1: Another kind of singularity people talk about a lot is the Big Bang singularity, and this is another kind of singularity, but it is 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 is 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. It's a singularity not in space, right, a black hole singularity and principles 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. So technically a singularity in the same sense of singularities is having infinities, but physically very very different from a black hole singularity.

00:46:02
Speaker 2: Was it spinning.

00:46:05
Speaker 1: We don't know. That would be the whole universe spinning, right, And we think probably the whole universe on average has spinned 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 thirteen point eight 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. So 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. Okay, this moment beyond which you can no longer calculate without knowing how to do quantum gravity sometimes called the plank 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 blue zero. This 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 plank scale.

00:47:14
Speaker 2: Do we know what temperature is absolute hot?

00:47:16
Speaker 1: Yeah, it's the plank temperature. It's a very big number.

00:47:19
Speaker 2: Oh okay, but it's not like five thousand. It's no, it's just some very big number, got it?

00:47:24
Speaker 1: 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. You don't find them often in the literature in general relativity. These are phrases made up by Kip Thorn and explained in his book The Physics of Interstellar Kip Thrn definitely knows a lot of general relativity, a lot more than I do, due to the total expert in 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 these words, and not all of 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 inflying singularity, he's talking about the complex space time structure inside a spinning or charge black hole. So 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 Kaushi horizon. So again these space times have more structure than just an event horizon and a singularity. There's this Kaushi horizon. Outside the Kaoshi horizon, you can actually survive like you can live. People have theories that you could have like stable orbits within the black hole, and maybe even life could evolve, which could be amazing. Within the Kaushi horizon, things get crazy. The Kaoshi 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 a singularity.

00:49:25
Speaker 2: Here, Okay, And so just to confirm it, 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 Cauchy horizon can't predict the future. It's us. We can't predict what happens in that situation.

00:49:46
Speaker 1: 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? Is to reflect the limit in our theory. There are some interesting physical effects here, like in falling radiation or matter. Blue shifts very dramatically as it approaches the Kushi horizon, and so the energy density diverges, like 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 inflying singularity. There's this other threshold after you come into the black hole, as you fall in towards the ringularity, you experience this inflying singularity of the Kushi horizon.

00:50:30
Speaker 2: 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. So what is an outgoing singularity?

00:50:39
Speaker 1: 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 nonlinearity of the Einstein equations lead to chaotic effects, and you can get things like proping gation of a curvature shock wave 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, so like huge gredients, 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.

00:51:21
Speaker 2: 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.

00:51:31
Speaker 1: You have not seen in Interstellar? Wow? Oh wow? And married to a nerd never seen that movie.

00:51:37
Speaker 2: He's never seen it? I know.

00:51:39
Speaker 1: Oh my gosh. Is that on purpose? You guys like boycotting that movie?

00:51:43
Speaker 2: No, just never no interest, just never got around to it. Maybe I need to.

00:51:47
Speaker 1: Well, there's lots of fascinating and wonderful stuff about that movie. It's also stuff I can't stand about that movie. So anyway, 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.

00:52:15
Speaker 2: Okay, got it all right.

00:52:17
Speaker 1: 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, but we don't really know, because sometimes the universe acts sort of nonsensical in a way that seems crazy at 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 popsie coverage.

00:52:46
Speaker 2: And thank you so much to Julie for inspiring this rousing conversation about the many kinds of singularities.

00:52:52
Speaker 1: Let's check in with Julie to see if we scratched her singular.

00:52:55
Speaker 3: Ititch consider my singular itch scratched, or maybe my reingular I did not know regularities were a thing. I like how you described 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. He also inspired new questions to ponder, like if there are fuzzballs instead of black holes, or if life could evolve inside a spinning or charge black hole. Wild and yep. I absolutely did read the Signs of Interstellar by Kip Thorne, which is where I got those terms, so it was helpful to have that terminology cleared up.

00:53:36
Speaker 4: Thanks again, all.

00:53:37
Speaker 1: Right, thank you very much everybody for tuning into this survey of several singularities. We hope this helps stretch your mind to the limits of what humans can conceive of.

00:53:46
Speaker 2: Until next time, Daniel and Kelly's Extraordinary Universe is produced by iHeartRadio. We would love to hear from you.

00:53:59
Speaker 1: We really we want to know what questions you have about this Extraordinary Universe.

00:54:05
Speaker 2: We want to know your thoughts on recent shows, suggestions for future shows. If you contact us, we will get back to you.

00:54:11
Speaker 1: We really mean it. We answer every message. Email us at Questions at Danielankelly.

00:54:17
Speaker 2: Dot org, or you can find us on social media. We have accounts on x, Instagram, Blue Sky and on all of those platforms. You can find us at D and K Universe.

00:54:27
Speaker 1: Don't be shy write to us