WEBVTT 00:00.000 --> 00:04.800 Thank you to Babel for supporting PBS.  Don't panic, but it's possible that an 00:04.800 --> 00:11.520 event horizon is forming right behind you right  now. Don't bother looking. You won't see it. It 00:11.520 --> 00:14.960 definitely won't look like the classic picture  of the black hole that you're probably familiar 00:14.960 --> 00:20.543 with. You won't even know that it's growing  to envelop you until it's way too late. 00:16.831 --> 00:22.911 for the universe's ultimate fate. Now onto the  episode. By now, we all have an idea of what black 00:22.911 --> 00:28.591 holes are supposed to look like. Discs of absolute  darkness on the sky, surrounded by gravity warped 00:28.591 --> 00:34.431 starfields, and the final electromagnetic screams  of stuff about to fall in. We think of the 00:34.431 --> 00:40.431 black hole as this roughly spherical surface of  lightlessness. And the name we give that surface 00:40.431 --> 00:46.591 is the event horizon. If I were to ask where  is the black hole, you might point to the event 00:46.591 --> 00:52.031 horizon. And that would be fair because a black  hole is really defined as something with an event 00:52.031 --> 00:58.191 horizon. The surface of no escape surrounding  a region so packed with mass and energy that 00:58.191 --> 01:04.911 even light becomes trapped. The event horizon is  as good a wear as anything for the black hole. 01:04.911 --> 01:11.471 And if I were to ask what is the black hole, it  seems fair to answer anything inside that horizon. 01:11.471 --> 01:15.871 Well, it turns out these answers are somewhere  between inadequate and just plain wrong. Even the 01:15.871 --> 01:22.031 question, when does the horizon exist isn't that  simple. Event horizons are actually much harder 01:22.031 --> 01:28.751 to pin down both in space and time. And when it  comes to black holes, a little bit of ambiguity 01:28.751 --> 01:35.711 can get you into a lot of trouble. So for safety  sake, let's get clear about the event horizon. If 01:35.711 --> 01:41.631 we define the event horizon as that surface from  which light cannot escape, we need to ask escape 01:41.631 --> 01:47.951 to where? One pretty reasonable answer would be  to require that in order to be considered above 01:47.951 --> 01:53.151 the event horizon, light has to be able to truly  escape, which means it must be able to get far 01:53.151 --> 01:58.511 enough away from the black hole that it no longer  is affected by its gravity. This is actually close 01:58.511 --> 02:04.831 to the formal definition. Light must be able to  reach infinite distance which is physics ees for 02:04.831 --> 02:10.991 very very far away. But this definition is already  at odds with how we tend to imagine the event 02:10.991 --> 02:18.511 horizon as the scary black disc or sphere. Let's  approach that disc then to investigate. We'll 02:18.511 --> 02:24.671 travel to the very near vicinity of what we think  of as an event horizon. Now, after collecting 02:24.671 --> 02:30.271 some Hawking radiation or whatever, we switch on  our ridiculously powerful rockets to move away. 02:30.271 --> 02:36.431 Because we carefully stayed above what looks to us  like the horizon, we're able to make some headway. 02:36.431 --> 02:41.871 But then, misfortune strikes. A giant asteroid  or something falls into the black hole from above 02:41.871 --> 02:48.351 us and the black hole grows in mass and the event  horizon expands and we're enveloped. But according 02:48.351 --> 02:53.551 to our earlier definition, if we or if light  cannot escape to an extreme distance, then we 02:53.551 --> 02:59.471 were already beneath the event horizon and we're  already doomed. Yes, something that black surface 02:59.471 --> 03:05.471 did expand to envelop us, but it wasn't the true  event horizon at all. So, let's dig a little 03:05.471 --> 03:10.991 deeper into the formal definition of the event  horizon because it completely changes the what, 03:10.991 --> 03:18.511 where, and even the when of our understanding of a  black hole. The textbook definition, the one that 03:18.511 --> 03:23.471 Steven Hawking and George Ellis sit down in their  book, The Large Scale Structure of Spacetime, 03:23.471 --> 03:30.671 is as follows. An event horizon is the boundary  of the causal past of future null infinity. The 03:30.671 --> 03:36.591 causal past of future null infinity. Okay, super  helpful. Well, we can break it down maybe a little 03:36.591 --> 03:42.351 further. We'll use a Penrose diagram. Longtime  viewers will remember these and it'll make 03:42.351 --> 03:48.911 things a little clearer, hopefully. Before we  complicate things by adding black holes, here's 03:48.911 --> 03:54.671 a Penrose diagram of an infinite flat universe.  Time increases upwards and one dimension of space 03:54.671 --> 03:59.951 is traced horizontally, but the contours of space  and time are curved so that the path of light is 03:59.951 --> 04:05.631 always 45°. And those lines are also increasingly  squished together towards the edges so that 04:05.631 --> 04:11.311 infinite space fits in this finite map. The points  at the top and bottom represent our infinite 04:11.311 --> 04:17.871 future and past. And the left and right points are  infinite spatial boundaries. But it's the diagonal 04:17.871 --> 04:24.031 edges of the diagram that we need to pay attention  to. These are the null infinities that Hawking and 04:24.031 --> 04:30.351 Ellis are talking about. In particular, the  future null infinity is where light rays end 04:30.351 --> 04:35.151 in the infinite future. And the past null infinity  is where they appear to come from if we trace them 04:35.151 --> 04:41.471 back in time forever. Now we can add a black  hole to the Penrose diagram like this. This 04:41.471 --> 04:48.031 is an eternal black hole. It was always there and  always will be there. It's just sitting out there 04:48.031 --> 04:53.551 to our left and any motion in that direction will  eventually reach it. And that means we can replace 04:53.551 --> 05:00.591 one future null infinity by the event horizon.  Below the event horizon, space and time grid lines 05:00.591 --> 05:06.751 actually switch place. Moving up on this diagram  is equivalent to falling deeper in the black hole 05:06.751 --> 05:13.151 towards the inevitable destination of the black  hole center. the singularity which occupies all 05:13.151 --> 05:18.511 future times inside the black hole. We have  previous episodes that explain all of this in 05:18.511 --> 05:23.951 more detail. With this sort of diagram, we can see  that nothing can escape the black hole. In order 05:23.951 --> 05:29.231 to escape, something would need to take a path  shallower than 45° and that means going faster 05:29.231 --> 05:36.031 than light. Even light gets stuck forever at the  event horizon if it starts there and inevitably 05:36.031 --> 05:41.311 at the singularity even if it was trying to  move outwards. Hawking and Ellis's definition 05:41.311 --> 05:46.831 is clearer in the context of this diagram. They  define an event horizon as the boundary of the 05:46.831 --> 05:52.911 causal past of future null infinity. This is  the future null infinity and its causal past is 05:52.911 --> 05:59.551 anything that can get to it traveling no greater  than light speed. That means the entire universe 05:59.551 --> 06:06.271 except the region below the event horizon. Nothing  behind that boundary can affect future infinity or 06:06.271 --> 06:12.751 indeed anything else in the universe that isn't  itself behind the same event horizon. Okay, so 06:12.751 --> 06:18.991 it feels like we're saying the same thing that we  already knew but with more words and more lines. 06:18.991 --> 06:24.831 But crucially, we we've now been precise enough  about black holes as a causal structure. There's 06:24.831 --> 06:29.631 something that determines what events are allowed  and forbidden in the universe. In doing this, 06:29.631 --> 06:35.711 we remove a lot of ambiguity that we ran into  earlier. But we also discover something really 06:35.711 --> 06:42.271 strange. The event horizon definition is no longer  local. It doesn't refer to a single location in 06:42.271 --> 06:48.031 space or point in time. It's the boundary below  which neither you nor light rays can escape to a 06:48.031 --> 06:52.831 great distance, aka reach future null infinity,  even if the black hole that eventually traps 06:52.831 --> 06:58.351 you hasn't started forming yet. So the event  horizon is a property of the entire spaceime 06:58.351 --> 07:03.071 reaching all the way into infinite future. It's  not just a statement about what is possible now, 07:03.071 --> 07:08.591 but what will be possible based on everything that  will happen to this patch of spaceime. Physicists 07:08.591 --> 07:14.431 sometimes describe the event horizon as being  teological from the ancient Greek term telos 07:14.431 --> 07:20.111 meaning final purpose. It tells us about the final  state of the universe, the paths that make it out 07:20.111 --> 07:25.631 to infinity and those that eventually end up stuck  inside the black hole. That's what I mean when I 07:25.631 --> 07:31.311 say that an event horizon might have just passed  you right now and you wouldn't even realize. Let's 07:31.311 --> 07:38.031 do another thought experiment to see why. We'll  start back on Earth. Relatively flat space free of 07:38.031 --> 07:43.791 black holes. However, for unfortunate reasons that  we don't need to get into, but may involve vogons, 07:43.791 --> 07:50.271 there's a spherical shell of radiation of light  collapsing towards us. This is an example of the 07:50.271 --> 07:58.431 Va spacetime devised by Indian physicist Prahalad  Vaja as a toy model to explore spaceimes and event 07:58.431 --> 08:04.271 horizons of a collapsing star without all of  the messy matter. In this thought experiment, 08:04.271 --> 08:09.711 it feels like there's no event horizon as the  shell of radiation converges on us. We don't 08:09.711 --> 08:16.031 even know that it's coming because no signal can  travel faster than the radiation zone collapse. 08:16.031 --> 08:20.991 It's ultimately going to form a black hole with  a radius governed by the amount of energy in that 08:20.991 --> 08:26.591 radiation. But according to our formal definition,  the event horizon forms long before the black 08:26.591 --> 08:32.191 hole. In fact, it grows from the center of the  collapsing sphere at the speed of light, reaching 08:32.191 --> 08:38.111 its maximum size when it intercepts the infalling  radiation. That's when the black hole truly forms, 08:38.111 --> 08:43.311 but the horizon was already there. To visualize  this, let's say that you're at the center of the 08:43.311 --> 08:48.751 collapsing shell and there's a lastditch effort  to escape. You shoot a lighteed signal out into 08:48.751 --> 08:54.191 space to see if any passing spaceships will  beam you up. If your signal makes it beyond 08:54.191 --> 09:00.031 the ultimate size of the event horizon before  the incoming radiation crosses that same point, 09:00.031 --> 09:07.151 then it escapes and maybe you hit your way out of  there. But if not, then it and you remain stuck 09:07.151 --> 09:14.351 behind the horizon. If you send your signal too  late, then it never reaches future null infinity. 09:14.351 --> 09:20.751 So by our definition, it was always behind the  true event horizon, trailing it as it expands 09:20.751 --> 09:27.471 to become a black hole. Let's see what the Penrose  diagram looks like for a Vega spacetime. It starts 09:27.471 --> 09:34.111 like our black hole-free diagram, which we'll  cut in half because who cares about this entire 09:34.111 --> 09:39.711 side of the universe? The sphere of collapsing  radiation looks like this single line in our one 09:39.711 --> 09:46.271 dimension of space. It eventually reaches us, but  the black hole it forms comes fully into existence 09:46.271 --> 09:53.231 when it collapses below that certain radius. The  event horizon is then a diagonal line upwards from 09:53.231 --> 09:59.631 that point. Just as in our black hole containing  Penrose diagram, the spaceime within that event 09:59.631 --> 10:07.231 horizon is terminated by a singularity. Now, it's  easy to see which light rays escape the forming 10:07.231 --> 10:13.391 event horizon and which don't. Ones that we send  out early enough to reach future null infinity 10:13.391 --> 10:18.191 are the ones that escape. Those that depart too  late fail to pass the involing radiation before 10:18.191 --> 10:24.591 the black hole forms. But these rays were doomed  from the very start. And so we need to trace the 10:24.591 --> 10:30.591 true event horizon backwards to encompass this  entire region. We have a part of the universe 10:30.591 --> 10:36.911 that is trapped even though it doesn't know that  it's in a black hole. So yeah, a nasonent event 10:36.911 --> 10:42.671 horizon might be forming behind your couch as  we speak. You might want to check that out. 10:42.671 --> 10:48.191 Although you'll have to wait until the end of the  universe before you can be absolutely certain. A 10:48.191 --> 10:54.911 secret event horizon could be due to the collapse  of something huge, a giant region of the galaxy 10:54.911 --> 11:01.631 or even the universe billions of years from now.  All of this is a weird way to think about event 11:01.631 --> 11:08.111 horizons, but does anything really change? Who  cares if we can't find the horizon? Well, the 11:08.111 --> 11:13.711 most obvious problem is that an event horizon is  used to define the boundary of a black hole. So, 11:13.711 --> 11:21.471 it makes it hard to talk about where a black hole  is. It contradicts our astrophysical intuition. 11:21.471 --> 11:27.471 We know that there is a black hole at the center  of our galaxy called Sagittarius A star and that 11:27.471 --> 11:33.471 stars will get eaten if they get within a certain  distance. But this local description feels at odds 11:33.471 --> 11:40.031 with the teological definition. This is even more  apparent when we try to simulate the merges of 11:40.031 --> 11:46.031 black holes on a computer. Because Einstein's  equations are difficult to work with in these 11:46.031 --> 11:52.111 highly dynamical regimes, we rely on simulations  to tell us what the spaceime will look like, we 11:52.111 --> 11:57.391 set up Einstein's equations to describe two black  holes in spiraling, then evolve the simulation 11:57.391 --> 12:03.151 forward in time until the black holes merge, and  we're left with a single black hole. But where 12:03.151 --> 12:10.591 and with what shape are the event horizons of the  merging black holes and of the final result? If 12:10.591 --> 12:16.991 a horizon is teological, then it's defined across  the entirety of the simulation to future infinity. 12:16.991 --> 12:22.591 We could get a single time slice out to see how  spacetime has evolved, but it won't tell us where 12:22.591 --> 12:29.871 the horizon is. We could possibly trace light rays  back in time from the end of the simulation and 12:29.871 --> 12:34.991 look for the boundary of a region from which no  light gets out alive. And that's very much in the 12:34.991 --> 12:40.351 spirit of Hawking and Ellis's definition. But this  is very awkward as a way to find black holes and 12:40.351 --> 12:47.551 not necessarily very instructive if we care about  the local shape of spaceime during the simulation. 12:47.551 --> 12:53.551 And besides, we still want to know what to call  that black surface that we think we're escaping 12:53.551 --> 12:57.631 but are really doomed because the real event  horizon is already above us. In the special 12:57.631 --> 13:03.151 case of a black hole that's done forming and will  never absorb new stuff, that black surface really 13:03.151 --> 13:09.151 is the event horizon in the technical sense that  we just defined. But in the real universe where 13:09.151 --> 13:15.151 black holes tend to keep growing, we need another  name for the current snapshot of the black holes 13:15.151 --> 13:22.751 boundary. And that name is the apparent horizon  where the formal event horizon represents the 13:22.751 --> 13:28.591 global inescapable boundary integrated across all  future time. The apparent horizon is a more local 13:28.591 --> 13:35.951 beast. It's the locally inescapable boundary,  the thing that you can't exit even right now, 13:35.951 --> 13:41.471 regardless of whether you can make an ultimate  escape. The formal definition of the apparent 13:41.471 --> 13:47.951 horizon is also in terms of what light rays can  do. But now it's not whether they can reach future 13:47.951 --> 13:53.871 null infinity. It's whether they can make any  progress whatsoever in the outward direction. 13:53.871 --> 13:58.191 Technically, we say that the apparent horizon  is the outermost surface from which all outward- 13:58.191 --> 14:05.631 facing null geodysics are converging inwards.  Having a local definition of the horizon is nice, 14:05.631 --> 14:11.231 especially because it lets us understand what  things look like if we're not at null infinity 14:11.231 --> 14:17.391 or otherwise really far away. When we see these  awesome simulations of merging black holes, 14:17.391 --> 14:23.871 what we're seeing is the evolution of the apparent  horizon. So why bother with the first definition 14:23.871 --> 14:30.271 of the event horizon at all? Well, it's because  the apparent horizon is relative. Every observer 14:30.271 --> 14:36.191 will agree on the definition of the true event  horizon, the ultimately inescapable region. But 14:36.191 --> 14:42.591 the definition of the apparent horizon varies not  just over time, but also with frame of reference. 14:42.591 --> 14:49.231 In relativity, your sense of now varies with your  velocity and the curvature of spaceime. Each sense 14:49.231 --> 14:55.631 of the present is a 3D spatial slice out of  the four-dimensional spaceime. And that slicing 14:55.631 --> 15:01.791 changes with perspective. The apparent horizon  will also change between these slicings. And it's 15:01.791 --> 15:08.111 even possible to find slicings or definitions of a  specially extended now that include a black hole, 15:08.111 --> 15:14.431 but in which the apparent horizon disappears.  But that's not true of the true event horizon. 15:14.431 --> 15:20.511 If you're behind that, it doesn't matter how  you slice spacetime, you are stuck. In fact, 15:20.511 --> 15:27.951 every possible apparent horizon is guaranteed to  always lie inside or on the actual event horizon. 15:27.951 --> 15:32.591 In this sense, the apparent horizon gives a  conservative estimate about the extent of the 15:32.591 --> 15:39.071 black hole. It also gives a much more useful way  to study the behavior of dynamical black holes. 15:39.071 --> 15:46.431 black holes that are currently feeding like in  quazars or in merging black holes. In that case, 15:46.431 --> 15:51.551 the apparent horizon does something quite  unexpected. You have these apparent horizons for 15:51.551 --> 15:57.231 the inspiraling black holes that warp as they get  close, but the apparent horizon of the final isn't 15:57.231 --> 16:03.711 just a smooth merging of the two. That larger  joint apparent horizon forms only in the instant 16:03.711 --> 16:09.551 that the event horizons merge. So, the apparent  horizon is far from a substitute for the event 16:09.551 --> 16:16.191 horizon. It's a genuinely different object with  its own interesting properties. So, what, where, 16:16.191 --> 16:22.991 and when is an event horizon? And is there one  forming behind you right now? Well, if you care 16:22.991 --> 16:28.431 about what's happening close to a black hole at  a particular time, then you need to get creative. 16:28.431 --> 16:34.911 You need to choose reference frames and ask where  for that observer light appears to turn inwards at 16:34.911 --> 16:40.191 the apparent horizon. But if you want the most  clear definition, the definition that matters 16:40.191 --> 16:45.871 if you want to escape a black hole, then the true  event horizon is not a property of local space or 16:45.871 --> 16:51.471 immediate time. It's a thing defined by the past  and the future and exists as a causal boundary 16:51.471 --> 16:58.271 cutting its way through spaceime. Thank you to  Bubble for supporting PBS. If you spend any time 16:51.471 --> 16:56.431 in learning a new language and sharing that with  five other people in your life, check out the link 16:51.471 --> 17:12.591 in the description for the Babel Group plan.  You can get up to 55% off your subscription.