Do black holes have a maximum electric charge?

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Speaker 1: Hey, or Hey, I've got a physics dad joke for you.

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Speaker 2: Well, is that a joke that's only funny to physicist dads.

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Speaker 1: Let's find out why do physicists complain about the price of protons.

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Speaker 2: I don't know what.

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Speaker 1: They think they've been overcharged.

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Speaker 2: I think I paid too much for that joke.

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Speaker 1: What do you mean it was free?

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Speaker 2: Exactly? I am positive I was overcharged.

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Speaker 1: Oh, that's such a negative reaction.

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Speaker 2: I am hory Ham, a cartoonist and the creator of PhD Commics. Hi.

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Speaker 1: I'm Daniel. I'm a particle physicist and a professor at UC Irvine, and I'm always trying to find the in this crazy cosmos.

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Speaker 2: What does that mean is? Do you think the universe is funny?

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Speaker 1: The universe is kind of hilarious, and you can respond to it either by being freaked out, like wow, this place is insane, or you can laugh at it and say like wow, somebody out there has a sense of humor when they put this thing together.

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Speaker 2: Oh, do you think the universe appreciates being left at what if it's not doing it on purpose?

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Speaker 1: I like to think we're laughing along with the universe. You know, we're not mocking it. We're appreciating the cleverness of its structure, which sometimes you know elicits a chuckle.

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Speaker 2: Yeah, But is it funny like funny haha, or is it funny like.

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Speaker 1: I think it's a big mixture of the two. It's sometimes pretty weird and that makes me laugh.

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Speaker 2: But anyways, welcome to our podcast, Daniel and Jorge Explain the Universe, a production of iHeartRadio, in which we.

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Speaker 1: Try our best to find the sense in the universe. We look out there at all the particles buzzing and frothing and doing all sorts of bizarre things and try to weave it together into a story. Something in our minds explains why electrons zig this way and why protons zig that way, and how they all come together to make this incredible, delicious, hilarious universe that we appreciate.

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Speaker 2: That's right, because it is a pretty curiously funny universe, full of amazing mysteries and contradictions sometimes and paradoxes, and here in the podcast we try to find the punchline to it all, just to deliver some lass and maybe also some mind blowing moments.

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Speaker 1: Sometimes what you need is humor to crack open a deep mystery of the universe. We'd love to joke our way into the hearts of black holes and understand what is the singularly most funny joke in the universe.

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Speaker 2: Well, my job is definitely to find jokes and write jokes. But are you saying that your job is also a joke?

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Speaker 1: No, you got to have a straight man on the podcast.

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Speaker 2: Right, Which in a physics podcast, which one is the straight man?

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Speaker 1: We're both straight men in one way and jokesters in another way.

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Speaker 2: We're both crooked. Is that what you're saying.

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Speaker 1: Look, I'm just trying to keep everybody out there awake. I've been getting all these emails from people saying they love to fall asleep to the podcast. And as much as I'm glad that people are finding some way to appreciate it, I hope they're at least staying awake to the end.

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Speaker 2: We're more of a meditation podcast. Is that where we are?

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Speaker 1: I'm trying to transition us from meditation to humor.

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Speaker 2: I think that's a big business. Actually, like podcasts that helps you fall asleep. I heard like a really good book to fall asleep. This is some kind of math book by Stanley Tushi or Tony Shlou one of those actors. They just read this math book really slowly and people found it and they found it a great way to fall asleep.

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Speaker 1: Great physics ASMR. Well, maybe when they sleep, one of our listeners will get a bolt of inspiration, an idea helps us crack open some of the mysteries of the universe. Or maybe that's too charged an idea.

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Speaker 2: I wonder if people are listening to us just as they are falling asleep, if we have a chance now to like implant ideas into their subconscious.

00:03:57
Speaker 1: Welcome to podcast inception right.

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Speaker 2: Send money to Jorge tomorrow. You will wake up refreshed and feeling alive and feeling like you and to Venmo me a few thousand dollars.

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Speaker 1: Maybe you're in a dream right now and this podcast isn't really happening.

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Speaker 2: Hopefully won't turn into a nightmare.

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Speaker 1: Hopefully you'll get a torrent to cash from the listeners.

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Speaker 2: But speaking of dark topics and scary nightmares, let's talk about black holes. Black Holes are notoriously I guess humorous in the sense that they are big mysteries and they seem to be full of contradictions inside them.

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Speaker 1: That's right, like dad jokes, black holes are some of the most extreme things in the universe. Instead of being the funniest things in the universe, they are the most massive, the most dense, the most gravitationally powerful things in the universe.

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Speaker 2: Would you say they're the holy grail of dad jokes? Or does that make too light over the gravity of the situation.

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Speaker 1: I think that was a massively successful joke.

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Speaker 2: Well, at least it doesn't suck us. I guess that's all black holes do.

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Speaker 1: Jokes aside, black holes are the most massively interesting things in the ar because we think they have within them some of the answers to the deepest questions in modern physics. What is a theory of quantum gravity? What happens when you take tiny particles and squeeze them all together so that they are gravitationally powerful? And so people are always trying to figure out a way to crack open a black hole to somehow peek inside and get a snapshot of those secrets of the universe.

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Speaker 2: Yeah, because it seems like black holes can eat pretty much anything, right, any kind of matter, any kind of light, any kind of energy. It can absorb even dark matter.

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Speaker 1: Right, black holes can certainly eat dark matter, that's right. And because everything out there in the universe has energy and energy means gravity, everything in the universe is attracted to a black hole. But there are of course always some caveats to that. If black holes have electric charges, you might be able to turn them from attractive into repulsive, and you might also weirdly be able to crack them open.

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Speaker 2: Yeah, that's another interesting thing that black holes can eat is they can eat electric charge. Right, Like, if you throw an electron into a black hole or a bunch of electrons, the black hole is going to gain a negative charge.

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Speaker 1: That's right, because charge is conserved in the universe. It doesn't just go away. So in the same way that when you add energy to a black hole, it gains in mass proportional to that energy, when you add a charged particle to a black hole, it gains its charge.

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Speaker 2: Do we actually know that, Daniel, Or is that just from the theory that the theory says that if you throw an electron in the black hole, now is a little bit more negatively charged or does charge maybe I don't know, decompose inside of a black hole and turn into energy.

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Speaker 1: That's definitely just from the theory. We're not even one hundred percent sure that black holes exist in the universe. We have a bunch of candidates that seem like black holes, but of course there's a whole bevy now of proposals for what they might be instead of black holes. But we think that charge is conserved in our universe, and so even if those particles transform into some other state, the electric charge is made. But again that's just theoretical. But that electric charge does create some very strange conditions inside and outside the black hole.

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Speaker 2: And I guess the question you can ask is how many electrons can you throw into a black hole? And is there possibly a maximum number of them that you can throw in?

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Speaker 1: That's right, because as black holes get more and more charged, they get weirder and weirder, and so if you can add an infinite amount of charge to a black hole, you might even be able to crack it open.

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Speaker 2: So to be on the podcast, we'll be asking the question do black holes have a maximum electric charge? Now, this is like how much they charge for people to go inside or what?

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Speaker 1: Yeah, I think we get a podcast discount though.

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Speaker 2: Oh yeah, two for one, two podcast hosts for.

00:07:50
Speaker 1: One because we've been featuring black holes on the podcast so many times. We're basically like friends of the black Hole. By now we're on the sort of special VIP list.

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Speaker 2: We're like the mater shells for a black hole, the black hole industry.

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Speaker 1: That's right, we're paid under the table by big black hole.

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Speaker 2: The problem is they can never pay us because nothing can escape a black hole. You have to go in there to get your money.

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Speaker 1: They tell us it's in there, but we haven't actually verified that.

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Speaker 2: Well, this is kind of a weird question. Can a black hole have a maximum electric charge? Which is weird to think about because it doesn't seem like a hole can have a maximum. A black hole can have a maximum of anything, right, Like, black holes can gobble mass and energy almost as much as it wants, as far as we know, right.

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Speaker 1: Yeah, there's no theoretical limit to the mass that black hole can have. There's some practical limits there because they have to actually absorb the stuff and has to fall in at the right angle, and sometimes black holes can create conditions that repel the stuff around them. So practically speaking, there does seem to be a limit to how big black holes have gotten in our universe. But Theoretically, there's no limit to how big a black hole can get. It can be billions of solar masses. It could be trillions of solar masses. It could be quadrillions of solar masses. It can keep inventing metric pre fixes, and black holes could theoretically grow to be that large. But that's not the same for a black holes spin or for a black hole's charge. As these black holes get more and more charged, that they get weird and they start to border on breaking the rules.

00:09:14
Speaker 2: Of general relativity, and then they get charged with the crime of breaking the rules. That's right, and they go to physics jail, But they're tracked with physicist dads for the rest of their existence, telling them bad dad jokes.

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Speaker 1: That's a terrible punishment. Absolutely, yeah, No, The punishment for going to physics jail is that you puff out of existence. Right. Going to physics jails means you've broken a law of the universe and therefore you no longer exist.

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Speaker 2: It seems kind of harsh.

00:09:39
Speaker 1: Hey, everybody knows the rules. These are just the consequences of your actions, man, But.

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Speaker 2: Don't you need to know the law before? I guess you can break the law? Without knowing it and still be guilty. It seems a little unfair.

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Speaker 1: Well, maybe people should listen to this podcast. We'll educate them about what the laws of physics are so they can avoid breaking the rules and go into physics jail.

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Speaker 2: No, no, then we're we're live, Daniel. They might sue us for, you know, not telling them the full story.

00:10:04
Speaker 1: Well, anybody who's broken the laws no longer exists, so they can't sue us.

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Speaker 2: Oh yeah, that's true too.

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Speaker 1: Well.

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Speaker 2: As usually, we were wondering how many people out there had thought about this question of whether black holes can have a maximum electric charge.

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Speaker 1: So thanks very much to all of you who volunteer to answer these questions. We really appreciate it. And if you would like to hear your voice on the podcast in the future, please don't be shy. Write to me two questions at Danielandjorge dot com and I will set you up.

00:10:30
Speaker 2: So think about it for a second. Do you think black holes can have a maximum electric charge? Here's what people have to say.

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Speaker 3: I do not think that a black hole would have a maximum electrical charge. I think it would all be dependent on how big it is, so I would think that the bigger the black hole is, the more the higher, like the maximum electrical charge would be.

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Speaker 4: I would have thought that a black hole would remain roughly neutral or probably no theoretical limit to the charge it could have. I do wonder if a high charge black hole could discharge with some sort of lightning. Perhaps.

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Speaker 2: If black holes can grow indefinitely, then maybe they can grow their electric charge indefinitely as well. All Right, a pretty interesting range of answers. Some people said maybe, some people said probably not, and some people said it depends.

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Speaker 1: I feel like these are all leaning towards the direction that black holes could have an arbitrary charge.

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Speaker 2: M Yeah, because I guess that makes sense, right, Like, if it can eat an infinite amount of mass, why can it have an infinite amount of charge.

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Speaker 1: Well, as we'll see, mass in charge are different, right, Mass tends to accumulate more mass and create more attractive gravity. It's not the same thing with electric charge, right. Electric charge can do things that mass can't do, like it can repel other charges. So it gets to be quite complicated.

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Speaker 2: Well, they gat to it, Daniel. Let's recap what a black hole is again.

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Speaker 1: The basic idea of a black hole and what we need to understand for today's episode is that it's a region of space where particles can never escape. So we talk about this thing called the event horizon, behind which things are hidden forever. What the event horizon really means is that there's a region of space that if a particle enters it, it will never leave. Like if you fast forward to the infinite future of the universe, that particle never escapes the event horizon. It's not like literally a physical barrier in that sense. It's just a region you draw in space and say, by the way we've done the calculation, anything that enters here never leaves. And the reason is that space time is curved so much by the mass of the center that the particles never escape. And it's important to understand that the event horizon is not something you can ever exactly say where it is right now. In order to really know where the event horizon is, you have to kind of do that calculation out to the future infinity and say, oh, these particles never escape, but those particles do escape.

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Speaker 2: But you can take a picture of a black hole, wouldn't that kind of tell you the size of it and to what extent the black part of the black hole is.

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Speaker 1: Yeah, you can take a picture of a black hole, and we've done it. We have a couple of really cool images, and you can see a ring of gas around it, and then at the center you see an area that isn't emitting any light. What I'm saying is that, mathematically speaking, or most technically in general relativity, the region around the black hole that we call the event horizon is something you can only ever determine, sort of like in the infinite future of the universe. Like, even if you're looking at the black hole and you see no light emitted from it, that doesn't mean that there isn't like some path for a photon to like graze just within it and eventually make it out. You sort of like can't call it the event horizon until all those particles have had their chance to escape and you can say which ones made it and which ones can't.

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Speaker 2: All right, So then it's a region of space where nothing can get out, not even light. But there's some debate about what's exactly at the center of a black hole and whether or not it's possible for something to be at the middle, or maybe it's fuzzier than people think.

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Speaker 1: Exactly in general relativity, we have this picture of the interior of a black hole is being very very curved in space time, which means everything falls towards the center. In fact, space time is so distorted that, like the timelike coordinate for these things, the future path of everything is just to head towards the center of the black hole, and that creates sort of a runaway condition where it gets more curved, and then things fall further in, which makes it more curved, and so things fall in no stopping it, and so eventually it just all coalesces into the densest possible point. In general relativity, we call this a singularity, and nobody knows if a singularity is real or if there are really singularities inside black holes. I think if you pulled a bunch of physicists, something like ninety nine percent of them would say singularities are not real, that this picture from general relativity is sort of like an indication that the theory has broken down, not like an actual physical prediction the singularities.

00:15:01
Speaker 2: Are there, right, But I guess it maybe depends on how you define a black hole, like is the black hole the region of space within the event horizon, or do you only call a black hole the singularity in the middle.

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Speaker 1: Well, we can never observe anything within it. So I think the operational definition of the black hole is something that creates an event horizon, and then there's a question of what's inside it, what has created that event horizon, and general relativity says, actually, any equal distribution of mass within the event horizon would cause a black hole. It's just that general relativity predicts that distribution of mass will collapse into a singularity. Other theories predict that it won't predict that. You have other sorts of weird states, like quantum mechanics says you can't have a singularity. It's too much information concentrated at one point. You know the location, you know the energy. It's just it violates the basic laws of quantum mechanics, and so various theories of quantum gravity predict like weird fuzzy blobs at the hearts of black holes. But the truth is we don't know, and we'd love to know, because that would help us build a deeper theory of the unit. It would help us understand how to unify quantum mechanics and general relativity. But frustratingly, those answers are all hidden within the black hole.

00:16:09
Speaker 2: Right, Like inside of the black hole, everything could be bunched up in the middle of the black hole, or maybe things are more evenly spread out, or maybe it's in some kind of fun, interesting flowery pattern of stuff inside of the black hole.

00:16:21
Speaker 1: Right. Yeah, we have theories of like fuzzballs from string theory. We have theories of gravitationally slowed down collapsing stars. We have theories where a black hole will eventually turn into a white hole. There's many, many theories for what might be happening inside them. The reality of what's happening inside there is probably something even weird or something that no existing human physicist has imagined. If we could crack these things open and see what was inside, probably we would all be shocked. It'd be one of those delicious moments of science when we're like, what is going on? That's impossible, And then of course we'd be scrambling to come up with explanations. But those explanations would give us the clue is to like, what's really happening. What space really is deep down is space a bunch of quantum things that have woven themselves together to make the universe or is something else going on?

00:17:12
Speaker 2: Yeah, and I guess the problem is that, you know, you can't study what's inside of a black hole because if you ever get inside of a black hole, you're never getting out. Or even if you can send a robot or something, the robot can send a signal because nothing, not even radio ways or light can escape the black hole. Right, that's the main problem.

00:17:29
Speaker 1: That is the main problem. But fortunately black holes are more complex than this picture. What we've talked about so far is basically just a dot of mass. It's not spinning, it doesn't have electric charge, it's just mass. And so in general relativity you call this a short style black hole. It's like the simplest possible model of a black hole. But we don't think that any of the black holes actually out there in the universe are like this. We think it's more likely that black holes have a little bit of charge and maybe even have a lot of spin that can really change what happens to a part of that comes near the black hole in sort of surprising ways, especially if the black hole ends up with a lot of charge.

00:18:07
Speaker 2: Interesting. So, usually people think of black holes as just absorbing mass, but maybe when it absorbs other things like charge or the spin of things. Maybe the picture changes, and so let's get into what those changes could be and whether or not divide. Let us open a black hole, but first, let's take a quick break. Or are we're talking about black holes and whether or not they have a maximum electric charge. I wonder if black holes have like a little battery meter to tell you when they're fully charged, or maybe they do, but you just can't see it because it's a black hole.

00:18:49
Speaker 1: I think if you overcharge a black hole, either you or the black hole or both might have to go to physics jail.

00:18:56
Speaker 2: Wait, why would the why would the black hole have to go to jail too? I mean, wouldn't it be the victim in this case because it was overcharged?

00:19:04
Speaker 1: You're right, it's totally not fair, but it would be the one breaking the rules. General relativity tells us that if you put too much charge in a black hole, weird, surprising, nonsense things might happen.

00:19:15
Speaker 2: Mm. But I guess the question is who's going to put the black hole in handcuffs? Is there physics police that is gravity proof?

00:19:24
Speaker 1: If there's physics police out there, I hope they're not policing my physics. Dad jokes, because then I am.

00:19:28
Speaker 2: In trouble, you'll get multiple life sentences. I'll do more physics.

00:19:34
Speaker 1: I hope to get off relatively lightly.

00:19:36
Speaker 2: Well, we know that if a black hole is a regional's face or nothing can escape, not even light, and so it's really hard to look inside of them. But only if you consider mask going into a black hole. If you consider other things going into a black hole, the picture changes, maybe to the point where you can open a black hole. So let's talk about some of these other things that can go in. One of them was a spin that's right. When we calculate the radius of the event horizon, our prediction for the region of space where if you enter it you're trapped forever. That calculation is pretty simple if the black hole.

00:20:07
Speaker 1: Only has mass, right, if it's just a dot of stuff and it's not spinning, so that's the short styled black hole. But if the stuff is spinning, and the calculation is a little bit more complicated, we call this a curb black hole KERR, and it has a different event horizon, like the radius of the event horizon of a spinning black hole is different from the radius of the event horizon of a black hole with the same mass, but that's not spinning. And you might ask like, well, how can black hole spin? What can you do to spin a black hole? Well, you know, angular momentum in the universe is conserved, and so if something hits the black hole with angular momentum, the black hole is going to have angular momentum. The same way if your friend pushes you, but they don't push you straight on, they push you like on your shoulder, it could spin you around. If an electron falls into the black hole but doesn't fall straight in, if it falls like a little bit to the side, then it's going to push the black hole a little bit and get it spinning.

00:21:01
Speaker 2: Interesting, that's a weird picture to think of a black hole spinning, Like can a hole spin? What would it mean for a hole to spin? Does that mean that the event horizon is spinning or just that the things inside of the black hole have kind of a general spin to it.

00:21:15
Speaker 1: Yeah, the event horizon is not itself a physical thing, right, it's a distance from the center, So in that sense, that part doesn't spin, but the mass inside the black hole is spinning. Now, a singularity a dot in space that has no extent that can't spin. Right, A true singularity with no volume can't have any spin because spin requires some length. So inside a black hole that is spinning, we don't think there is a singularity. General relativity predicts something else. It predicts a ringularity, a little ring of singularities that's spinning. So that's what's sort of like keeping the spin alive. That the event horizon you can still calculate at some radius, and the space around the black hole now gets weird. You get frame dragging effects. So we've talked about a few times on the podcast. So in Einsteiny and gravity, it matters whether something is spinning or not. You have a different gravitational effect.

00:22:08
Speaker 2: So if your black hole is spinning, it doesn't have a singularity in the middle like a point you're saying, it has like a weird.

00:22:16
Speaker 1: Ring, Yeah, a ringularity.

00:22:18
Speaker 2: So then does the event horizon also change shape or is it still a sphere.

00:22:22
Speaker 1: The event horizon itself is still a sphere, but now you have a region around the event horizon called the ergosphere where things get weird. We talked to once in a podcast about whether you can extract energy from black holes, and in this ergosphere, which is sort of a doughnut shaped region around the black hole. The black hole will make things spin in a weird way, and you can use that to extract energy from the black hole. So a spinning black hole has sort of two different regions. Is this spherical event horizon and then there's this doughnut shaped ergosphere around it.

00:22:51
Speaker 2: Where space time is curved differently or is it all still curved like a sphere? Like what does this ergo sphere do?

00:22:58
Speaker 1: So space time is different inside the ergosphere and not inside the ergosphere, and it's different in this sort of a complicated way. It's always, of course pointing towards the black hole. If you're in the ergosphere, you're going to feel a gravitational pull towards the black hole. But if you're in the ergosphere, you also feel other effects because space time has this frame dragging thing happening to it, which is sort of counterintuitive because we think of gravity as like just attractive it just pulls you towards stuff. But this frame dragging effect can actually also create a spin. Remember that we've measured this frame dragging effect using gravity Probe B. This satellite that orbits the Earth with super hyper precise gyroscopes that measure these kinds of spins. So if you're within the ergosphere or near any spinning object, Einstein says, you're going to get a little bit of a twist as well as a pole.

00:23:45
Speaker 2: Interesting. Now, let's talk about charge, because you said you can also change the properties of a black hole by throwing in charge. And this happens when you throw in charge objects into the black hole, like electrons. If you throw an electron in the black hole is going to gain a negative charge.

00:24:00
Speaker 1: Yeah, so you take a black hole and you toss in an electron, it'll happily gobble it up. But that charge doesn't just go away. Right, the electron had an electric field, and just before it fell into the black hole, there was an electric field there. Now that electron has gone inside the black hole, there's still an electric field there. Right, it's sort of frozen in time from the last moment just before the electron crossed the event horizon. No more information can update it. Like what the electron does within the event horizon can't change the electric field. And so there's an electric field there, and you can ask like, well, where does that come from? Well, the whole black hole now has an electric charge.

00:24:37
Speaker 2: Like from a distance, if you were to see a black hole up ahead of you, you would suddenly deteg that it's a little bit more negatively charged, right Like if you had a magnet, it would be a little bit more attracted to it. Perhaps if you had a positive charge, you'd feel more of a pull towards the black hole exactly.

00:24:54
Speaker 1: And the super weird thing is, think about what happens to the next electron. So you have like a bag full of electric as you throw one in, Now your black hole has a negative charge. Now electron number two, what happens to it, Well, it feels a gravitational attraction from the mass of the black hole, but now it feels an electrostatic repulsion from the charge of the black hole. The black hole is negatively charged, so just like the electron that fell in, it's going to repel electron number two. So electron number two feels an attraction towards a black hole and a repulsion as well.

00:25:25
Speaker 2: Right. Interesting, It's sort of like if you are collecting electrons in your pocket. At some point it'd be harder to throw another electron in because you have so much a negative charge in your pocket. That adding another electrical negative charge would be hard to.

00:25:39
Speaker 1: Do exactly, And this is why I mentioned earlier like mass and charge are different. Mass just attracts itself. The more mass you have, the more mass you're attracted to, the more it pulls on other masses. But charge is different. Right, if something accumulates a lot of negative electric charge, it will then repel other things with negative electric charge, and that has a really important consequence for where the event horizon is. If you try to solve all equations and calculate, like, well, where is the event horizon for a black hole with or without an electric charge? You discover that a black hole with an electric charge has a smaller event horizon.

00:26:12
Speaker 2: Well, it's only pushing away other negative electric charges. But like for if you're a positron or a positively charged particle, now your really negative black hole is more attractive. So it wouldn't the event horizon grow for a positively charged particle.

00:26:28
Speaker 1: Well not exactly. There are two things going on here at once. First, the event horizon radius does depend on the charge of the black hole. Right, as the charge of the black hole increases, the radius shrinks, and we're tempted to say that that's because of the electromagnetic force from the charge now working against gravity, right, gravity pulling things in and the electromagnetic force pushing things away. But that's not actually what's happening when it comes to the event horizon. If it were, it would mean that the event horizon would be different for different charges of particles. Positive, neutral or negative particles would see different event horizons. But it isn't. It shrinks the event horizon for all particles, regardless of charge. And unfortunately there's not a very simple intuitive way to understand that. I actually talk to a bunch of GR experts, and the best I can do is to tell you that the size of the black hole is affected by the electromagnetic energy that's inside the event horizon. But it's not in a simple way. Remember that GR is based on the stress energy tensor, and it's not just that more energy means more curvature. It's quite complicated, and in the end, the greater the charge, the smaller the event horizon. But the second thing is that the black hole charge does push or pull on particles outside the event horizon, and that does depend on the charge of the particle. So a negatively charged black hole can resist negative particles from ever crossing over the event horizon, and it can accelerate positively charged particles towards it. The event horizon is the same for all of them, but the black hole charge can prevent some particles from crossing it, or it can assist them. What I think is super fascinating is that the event horizon is shrinking as the charge grows. So you toss in an electron and the event horizon shrinks, and then if you cram another electron in there, the event horizon shrinks further, and so you can keep going. You keep going, and there's a point where you have so much charge that essentially you erase the event horizon.

00:28:29
Speaker 2: WHOA, Okay, Now I think you're imagining a scenario where you only put electrons, Like you make a black hole out of electrons, and you only put more electrons in it, and then you ask, what does that black hole look like to another electron? So, now, like, if you do the math, does it work out that it does erase the black hole to an electron? Because I imagine if there's a singularity in the middle of the black hole, then you sort of can't beat a singularity, can you.

00:28:55
Speaker 1: That's exactly the question, right, And so people have been doing these kinds of calculations, and according to general relativity, there's a maximum charge that a black hole can have, and if you manage somehow to give it more charge than that, then effectively there will be no event horizon. You've removed the event horizon. You revealed the singularity. Like you sit down and do the calculations. The radius of the event horizon depends on the mass enclosed in the black hole and on the charge of it. And if the charge gets above a certain number relative to the mass, then there's no solution. Right. As the charge grows, the radis event horizon shrinks and shrinks and shrinks and shrinks, until eventually it's at zero. And that's what we call the maximum charge the extremal black hole. And if you somehow added another electron to that, nobody knows what would happen, Right, would you get a naked singularity? Would we all go to physics jail? Nobody knows. Let's find out.

00:29:52
Speaker 2: Well, I guess I imagine the math is complicated because an electron also has mass. Right, So if you throw an electron into a black hole. Well, you are increasing the mass of the black hole, making it more of a whole, but you're also making it more repellent to other electrons. And you're saying that the way it works out is that electrons maybe have more charge than they have mass, and so therefore if you make a black hole out of just electrons, it is going to repel other electrons.

00:30:17
Speaker 1: Yeah, there's sort of two parts of the question. One is like, assume that somehow you can get enough electrons in there, what would happen? And the answer to that question is nobody knows. Right, nobody knows what would happen. It predicts basically a naked singularity. And there's been a lot of discussion in theoretical physics for a long time about like, hmm, this seems weird. Would the universe actually allow this or would something stop it? And Roger Penrose has this idea called the cosmic censorship hypothesis that says something is going to intervene. There must be a reason why this is impossible, because you can't have a singularity just out in space. Naked singularity is like an anathema to particle physicists or to theoretical physicists, so they imagine something must prevent from happening. And then the other question, the second question, or the other part of it, is could you actually ever create this situation? Is there something preventing us? What could be preventing us from getting enough electric charges altogether, all at once?

00:31:14
Speaker 2: But again, I feel like this is only if you're an electron. The black hole disappears only if you're an electron. But like, light still can't escape this all electron black hole, right because light is neutral, Right, Like light doesn't carry you have a lot of negative charge in it.

00:31:30
Speaker 1: The black hole charge only affects charged particles on the outside of the event horizon, so it prevents more electrons from falling in, but it doesn't prevent photons or protons or other positively charged particles from falling in. But remember that the event horizon is the event horizon, and the radius of the event horizon is the same for all particles charged or neutral. Having a charge on the black hole shrinks the event horizon for all particles.

00:31:56
Speaker 2: But if you were I think maybe the point is that if something has a negative electric charge, it could maybe escape what we see as the black hole.

00:32:04
Speaker 1: I think the more accurate way to say it is that outside the event horizon, electrons would be repelled by the charge, but photons could still fall in once they pass the event horizon. It doesn't matter what the charge was, and all particles of any charge see the same event horizon.

00:32:20
Speaker 2: And protons would see us super duper extra huge event horizon.

00:32:24
Speaker 1: Right, Not exactly. It's true that outside of the event horizon of a negatively charged black hole, protons would feel a strong attraction from the electromagnetic force and get pulled in towards the event horizon. So at some distance outside the event horizon, electrons are repelled and protons are attracted towards it. So it sort of effectively sweeps up more protons at larger radii than electrons. But the event horizon isn't actually different. The point of no return is the same for the two particles outside the event horizon. It's still possible for those protons to avoid falling in if if someone comes along and zaps them with energy to push them back away from the event horizon. But there's another outcome which is super weird, which is that black holes which are charged can repel each other, like in our universe. We see black holes eat each other, they attract each other, they gobble each other up, they form a super black hole. But if you had two negatively charged black holes, they would actually repel each other right the same way two electrons do, and if it had enough charge, they would avoid falling in together. You might even get them into like a stable configuration where these two forces are in balance and they could orbit each other.

00:33:35
Speaker 2: Now what I said earlier, is that true. Like if we see a black hole, it looks like it has an event horizon. It has a certain radius to the black sphere, but if it happens to have a lot of negative charge, that means that something could escape what we see as the neutral event horizon.

00:33:50
Speaker 1: Yeah, exactly. Remember the event horizon not a physical barrier. It's just like the limit where we say nothing that passes this will ever escape. But it's just determined by whether particles do or do not escape. So it's interesting because the event horizon is at the same place for all of the particles, electrons, photons, protons. If they pass it, there's no coming out. But electrons, photons, and protons are more or less likely to fall into that event horizon because of their charge. Technically, that doesn't change the location of the event horizon, but it does mean the fate of particles depends on their charge. There are some places near a negatively charged black hole where electrons cannot go because of their negative charge. They'll get repelled, but protons can. They are attracted, so protons will fall in and eventually get past the event horizon, but electrons will never reach the event horizon.

00:34:41
Speaker 2: I feel like we've just kind of destroyed the definition of the holes a little bit because we've usually talked about black holes as saying, you know, region of space where nothing, not even light can escape. But it sounds like it sort of depends on the charge of the black hole.

00:34:53
Speaker 1: Yeah, it does depend on the charge of the black hole. And in practice this isn't that big a deal because we think that most black holes don't have a lot of charge. I mean, things out there in the universe tend to be mostly neutral, like stars are mostly neutral, the Earth is mostly neutral, and that's because the electromagnetic force is pretty strong. So if a black hole somehow ends up with a significant charge, it's going to end up very powerfully attracting the opposite charge, like it will pull very hard on protons flying nearby and suck them up and end up being neutralized. So the electromagnetic force, because it has two charges and is very powerful, tends to mostly neutralize stuff. So we don't think this is something that happens very often in the universe, very very charged black holes.

00:35:37
Speaker 2: Yeah, I guess that was kind of the earlier point that you were trying to make, which is that maybe it's impossible to make these super duper charged black holes. And so let's get into the scenarios that you would need to make a repellent black hole, a super negative black hole, and what would it mean about the laws of the universe. So let's dig into that. But first let's take another quick break. All right, we're talking about black holes and whether or not you can make one disappear in a way by overcharging it, by putting so much electric negative charge into it that it actually starts to repel other negative charges, and so to an electron, the black hole just kind of disappears. Now, theoretically, you're saying that this is sort of possible, Like if I can construct a black hole with enough negative charge, it would sort of disappear. There wouldn't be a black hole.

00:36:37
Speaker 1: Theoretically, yeah, theoretically according to general relativity, which again we know is probably wrong about what's going on inside a black hole. But if you follow this theory, it says that if you did somehow manage to add enough charge to a singularity, then the event horizon would shrink down to zero. You essentially would reveal the singularity to the universe. You have a naked singularity.

00:37:00
Speaker 2: Well, meaning like I'm neutrally charged overall, all of my particles are canceling each other out, So like this black hole would still be deadly to me. I would still die going into it. But maybe if I was made up of only electrons, I could get out.

00:37:14
Speaker 1: If you were made of electrons, you would be repelled by it, so you'd have less chance to fall in again. Depending on the charge of the black hole, and if the black hole is charged, it would have a smaller event horizon, so you could get closer and still escape, but once you cross the event horizon, you aren't coming out. I still would not recommend a trip to a highly charged black hole, even if you could shoot electrons at it and have them survive. But this is a real opportunity for physics to try to figure out, like what happens. Does this mean that something weird would actually happen in the universe, or is there some reason why this is not possible, something like preventing this from occurring. I remember there's been lots of times in theoretical physics when they predicted something really weird they thought, well, that certainly can't happen. There must be something preventing it. Like black holes, which for a long time people imagine or a ridiculous prediction of general relativity in the universe must somehow arrange for them to never exist, but then we think we see them. So the question for super charged black holes and like naked singularities is like, is this something which could actually happen, you could really do this and see it, or is there some reason why it's impossible to set this thing up this way?

00:38:23
Speaker 2: Yeah, I think what you're saying is that we probably don't see a lot of super negatively charged black holes out in the universe. And so there's two possibilities. One is that there's something theoretical, some kind of fundamental law in the universe that prevents that from happening. And there's also maybe more practical limitations or barriers making this, Like you just can't practically make a black hole like this because you can't aggregate enough negatively charged stuff together practically speaking, from what we have in the universe exactly.

00:38:52
Speaker 1: And it's fascinating if the practical limitation is sort of what saves us from the principled problem, I would say, like, wow, this would be a crazy we'd all go to physics jail if this happened. And then it turns out, well, you can't actually build that kind of thing, Like there's no theoretical reason why it can't exist, but you couldn't ever assemble it. That's really fascinating the insight into like how the universe protects itself from going to physics jail. And so there's been a bunch of papers over the last twenty years trying to do this calculation. Like heuristically, you can imagine, all right, as I tossed electrons in, the thing gets more negatively charged and that makes it harder to toss in the next electron. Right, But people have sat down and actually done this calculation, which turns out to be quite complex, and papers over the last few years have concluded that the self force from the black hole. As the black hole gets more and more negatively charged, it will repel those electrons and it will prevent more charge from falling in before it hits this sort of maximum before the event horizon decreases to zero.

00:39:52
Speaker 2: Right, that's the practical. Although, what happens if you shoot an electron with like super fast, Like if I shoot an electron in towards the center of the black hole with enough energy, want it overcome the electric repulsion and get close enough to the black hole where it gets sucked in by gravity.

00:40:09
Speaker 1: Yeah, I love that your temptation is to like try to break the rules and like build an electron gun and shoot it at a black hole just to see what happens. That's exactly what leads us down the road do great discoveries. And so you know, the way to think about it is that anything that manages to fall into the black hole is basically going to have more mass than charge. Like, anything that falls in, it's going to have some mass, and so it's going to make the black hole bigger, which is going to allow it to have more charge without sort of like going over this threshold. And so basically anything that manages to fall in has to have a certain mass to charge ratio. And as soon as you get above the place where electrons can no longer fall in, then you're asking like, well, couldn't you force them in? Couldn't you like build an electron gun that makes them go super duper fast and forces them in? And effectively, what you're doing there is you're adding more energy to the electrons, and when the black hole eats that electron, now it gets even more energy and that adds to its mass, and so that keeps it from going over the limit. So if you shoot super high energy electrons at it, that energy keeps it from going over the threshold.

00:41:10
Speaker 2: Keeps it from going over the threshold for its size. But if I grow the black hole, then it can have more negative charge, right.

00:41:18
Speaker 1: Yeah, exactly, So anything you can squeeze into a charge black hole has to grow its mass more than its charge effectively in order to keep it from violating this limit. And practically it turns out you can't actually shoot anything to a black hole to break that limit. Anything you can actually get into the black hole would have to have more mass than charge or more energy than charge.

00:41:40
Speaker 2: Equivalently, So it sort of sounds like you're saying that I can shoot more electrons into a super negatively charge black hole. I just have to give it enough energy and then it'll get sucked in exactly.

00:41:49
Speaker 1: So technically there's no maximum charge to a black hole. There's a maximum ratio. Like for a given mass, there's a maximum charge. If you make it more massive, then yeah, can have more charge, but you can't have more energy in the charge effectively than in the mass. So there's no like absolute number that says black holes can't be more charged than this, But there is a ratio of the charge to mass for a black hole.

00:42:13
Speaker 2: So it's kind of a complicated maximum charge than an electron a black hole can have, Like I think you're saying, like, for a certain size of black hole, you can't just throw any electron in. It has to be an electron that has more mass or more velocity or energy than it has charge. So really there's no limit to the maximum charge of a black hole. It just starts to limit the kinds of electrons you can throw in.

00:42:38
Speaker 1: Yeah, things which would violate this ratio, Things that have like a lot of charge but almost no mass, would not end up in the black hole because they would be repelled by the black hole's charge. So things that would put this black hole in physics jail can't actually fall into the black hole.

00:42:54
Speaker 2: But to some kinds of electrons, to like slow moving electrons. I think you're saying that the black hole does kind of disappear and for them, the singularity is sort of exposed.

00:43:04
Speaker 1: No, slow moving electrons would be repelled by this thing, right, They wouldn't have enough energy essentially to get in there.

00:43:10
Speaker 2: Well, that's what I mean, Like the event horizon disappears for them, right.

00:43:13
Speaker 1: They would never even be able to enter that region of space.

00:43:16
Speaker 2: Yeah, But I think what you're saying is that there's maybe like an electron out there for a certain black hole with a lot of negative charge that could get into the regular event horizon, go right up to the singularity and then come back out because it has just enough more electric charge and mass for it to be able to get out again.

00:43:35
Speaker 1: Yes, for an extremal black hole, but then that electron would be forced out. It wouldn't be able to join the singularity and reveal the Singularity to the next electron. Like that event horizon still has to be non zero. There's no way to get that last electron into the singularity to make the event horizon actually have zero redius for the next one m.

00:43:55
Speaker 2: So let's maybe dig into what you mean by physics to jail and breaking the law. Why exposing a black hole's singularity break the laws of physics?

00:44:04
Speaker 1: Yeah, it's a great question. We don't really know what that means. General relativity has no solution there. It's like you try to solve the equations and you get the square root of a negative number. So now what's the radius of the event horizon. Well, we don't really know, right. General relativity basically breaks down there. It doesn't know what to predict. It can't even predict things as nonsensical as a singularity. There's just really no prediction there. And so we don't really know what would happen according to general relativity in that regime. And that's sort of the bigger story that general relativity isn't predicting singularities orringularities or post extremal black holes. It's really breaking down here. It's saying it can't make any predictions. The sign of an infinity or you know, like square roots of negative numbers in the theory is telling you that you've gone beyond the limits of that theory, that it's an approximate theory, and you've pushed it into a territory where it does not belong, where it cannot make any reasonable predictions.

00:44:57
Speaker 2: Hmmm, well it would break I guess our theory of it. But that's also assuming the universe follows our theories, Like maybe it could do. It would just break our math.

00:45:05
Speaker 1: Yeah, it would break our math. Certainly, something would happen, right, the universe probably wouldn't disappear in a puff of logic. If you did somehow force an electron inside an already extremo black hole, something would happen, and whatever that would be would be a great clue to tell us, like what's really going on. It would force the universe in some sense to reveal what its true laws are, you know, And that's what experimental physics is all about. It's like forcing the universe in a corner where it has to give up some secrets, or it has to tell us what happens in this situation, which gives us some answer. Maybe it would reveal some weird naked singularity and we'd learn how to modify general relativity, or maybe you would explode, or maybe you would turn into a wormhole, or we just don't really know. But whatever happened in that situation would be a huge clue towards solving quantum gravity, to understanding what happens when things get very very small and very very gravitational.

00:46:00
Speaker 2: All right, well, it sounds like the answer to our main question then is do black holes have a maximum electric charge? And it sounds like the answer is sort of like it has a maximum electric charge for certain other electric charges, but not others. It doesn't have a maximum electric charge in terms of how much charge any black hole can be because you can have maybe infinite electrical charge if you have an infinitely large black hole.

00:46:24
Speaker 1: That's right. If you want to charge up your black hole, you also got to make it massive at the same time. That's the recipe for charging up your black hole. You can't just take your black hole and add charge without adding mass. That would break the rules of the universe.

00:46:37
Speaker 2: Well, it would break the rules of the practical universe. But theoretically, you know, if if I was you know, if I had a cart blong on doing anything I wanted in the universe, could I create a universe with suddenly a super duper extra charge black hole for its mass to appear.

00:46:53
Speaker 1: Yeah, I think there's no theoretical reason why that arrangement cannot exist. There's just no theoretical way to build it. Starting from a universe and creating that configuration seems to be impossible. Though the actual configuration itself isn't technically impossible, right to put enough electrons in the same place where you lelate that condition. But practically speaking, we don't know of any way to build it. But if you were somehow able to do it, we would break the laws of our universe as we understand it, but we'd learn more about the true laws of the actual universe.

00:47:25
Speaker 2: Well, you wouldn't break the laws of the universe. You would just kind of break the practical laws of the universe. It'd be unexplained, Yes, it'd be unexplained. Like if you came across one of these things in space, you'd have no way of explaining how it got there.

00:47:38
Speaker 1: And that's important, right. We look out in the universe, we see stuff, We see atoms out there and all sorts of different elements, and we want to explain, like how do we get to this state? You start from the Big Bang, How is it possible to build all these heavy metals, and we have theories for how that happens. Everything that's out there in the universe, we look for an explanation for how it was made, how it was assembled, and so this would be a big.

00:47:57
Speaker 2: Mystery, unless, of course, it was just a bunch of this is Dad's telling negative jokes that I'm imploded into a super overcharged black hole.

00:48:06
Speaker 1: I hope they all collapse in shame.

00:48:08
Speaker 2: All right, Well, we hope you enjoyed that. Thanks for joining us, See you next time.

00:48:21
Speaker 1: Thanks for listening, and remember that Daniel and Jorge Explain the Universe is a production of iHeartRadio. For more podcasts from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or wherever you listen to your favorite shows.