the event horizon of the black hole space and time have fundamentally changed even professional physicists disagree on what we expect to happen there but there is a powerful tool in physics that can give us real intuition into the true nature of the event horizon it's time you learned it [Music] black holes objects with densities so high that there's this region the event horizon where the escape velocity reaches the speed of light nothing that falls below the event horizon can never escape and is lost to the universe forever while we see in falling objects freeze as time stands still at the horizon and anything that happens below the event horizon stays below the event horizon that's the official sanitized public version it's not entirely inaccurate but the reality is of course a good deal more complex and interesting even ignoring the complications of Hawking radiation or black hole rotation or growth a simplest black hole of Einstein's general theory of relativity purely gravitational static and eternal is a subtle and misunderstood beast but we can come to a powerful and intuitive understanding of the beast today I'm going to teach you how to use the same tool that physicists use is a tool that will less easily answer the most common questions about black holes for example our objects falling through the event horizon really physically frozen there from the point of view of the outside universe when you see the entire future history of the universe planed fast forward at the instant that you crossed the event horizon and do you see anything at all once you're inside the black hole the tool that will answer these questions is called the Penrose diagram sometimes also the Carter Penrose diagram it's a special type of space-time diagram designed to clarify the nature of aizen's but first a quick refresher on basic space-time diagrams by graphing time versus just one dimension in space we can look at the limits of our access to the universe due to its absolute speed limit the speed of light with the right choice of space and time units the speed of light becomes a diagonal line on the space-time diagram the area encompassed by the so-called light like paths defines all future events or space-time locations that we could potentially travel to or influence constrained by the cosmic speed limit that's our forward light cone our past light cone defines the region of the past universe that could potentially have influenced us let's drop a black hole onto our space-time diagram it lives at x equals zero on the space axis but exists through all the x on the graph it has a point of infinite density the singularity and an event horizon a bit further out the mass of the black hole stretches space and time so that light rays appear to crawl out of the vicinity of the event horizon before escaping to flat space-time no longer following 45-degree paths now let's throw a monkey into the black hole as it approaches the event horizon its future light cone bends towards the black hole as fewer and fewer of its possible trajectories lead away below the event horizon all possible trajectories lead towards the singularity the problem with the regular space-time diagram is that the path of light and the shape of the light cone changes as space-time becomes warped that makes it difficult to figure out what parts of the past and future universe the monkey can witness or escape to and this is where the Penrose diagram comes in it looks like this it transforms the regular space-time diagram to give it two powerful features it crunches together or compactify as the grid line is to fit infinite space-time on one graph very useful for black holes it also curves the lines of constant time constant space in what we call a conformal transformation so that light always follows a 45-degree path that means light cones always have the same orientation everywhere super handy for understanding monkey trajectories this is the Penrose diagram for flat space-time with no black holes same as with the regular space-time diagram blue vertical ish lines represent fixed locations in one dimension of space and red horizontal if slides are fixed moments in time now those lines get closer and closer together towards the edge of the plot to encompass more and more space-time they're extremely finally separated at the edges so that any tiny stretch on the graph represents vast distances and/or times the lines also converge together towards the corners so that light travels a 45-degree path everywhere on the diagram so a light ray starting from really really far away and coming towards us hugs the edge of the diagram and crosses an enormous number of time and space steps only reaching us in our very distant future okay let's drop a black hole into this space-time nice and safely far off to the left and because we only have one dimension of space any motion to the left brings us closer to the black hole its event horizon becomes the end of the line in that direction the future cosmic horizon on the Penrose diagram is replaced with a plunge into a black hole the compactified grid lines there now represent the stretched space-time near the event horizon an entirely new Penrose region represents the interior of the black hole weirdly the lines of constant position and constant time switch space flows at greater than the speed of light inwards towards the central singularity it becomes unidirectional flowing inexorably downwards just as time flowed inexorably forward in the outside universe all paths lead to the inevitable singularity once you're beneath the horizon your future light cone still represents all possible paths that you could take all of them end up at that singularity the only way to escape back to the outside universe would be to widen your light cone by traveling faster than light so you're out of luck now that we've nailed the Penrose diagram we can use it to do some serious black hole monkey physics our spacefaring simian begins its journey and emits a regular light signal that we observe from a safe distance as it approaches the black hole these light rays have further and further to travel through increasingly curved space-time and so the interval between receiving signals also increases the progress of the monkey appears to slow to a halt very close to the event horizon and the final signal at the moment of crossing never reaches us is trying to travel at the speed of light against a Lightspeed cascade of space-time with this picture we can start to answer some very serious questions first what would happen if the monkey remembered to fire its jet pack of the last instant before reaching the event horizon where it could still escape its future light cone still includes a tiny sliver of the outside universe it had better be a good jet pack because it's going to need to follow a very long near light speed path away it will nonetheless have experienced far less time than us when it emerges into flat space-time in our far future assuming no jet packs the monkey is probably doomed to a graceful reverse swan dive through the event horizon watching the entire future history of the universe play out above it at that last instant yeah actually you know it doesn't see that at all the monkeys last view of the outside universe is defined by its past light cone that encompasses all of the light that will catch up to it and that light is stuck following these diagonal lines because it has to contend with the same stretch space-time as the monkey there's no future universe spoiler promo if it could instead hover above the event horizon then it would see the universe in fast-forward although that view would be compressed into a small circle directly overhead watching the monkey frozen on the event horizon is going to make us feel a bit guilty after a while could we change our minds and launch a daring monkey rescue mission sadly no even if we could travel at the speed of light after a certain point there's no catching the monkey we would see it suspended above the horizon as we race in to meet it but it'll always appear to be just a little further ahead no matter how close to that horizon we dare to go remember the monkey isn't actually above the horizon for infinite time it only appears that way to us because as long as we're outside the event horizon no times that we can witness correspond to the monkey crossing that horizon in order to see that crossing we would have to cross the event horizon ourselves once inside the black hole we could potentially see the monkey below us all space-time within the black hole is flowing toward the singularity faster than the speed of light but two neighboring radial layers aren't traveling faster than light relative to each other that means that the monkey signal can still reach us although it might be more accurate to say that we catch up to the monkeys outgoing signal but even that's so-called outgoing light is still moving downwards doomed to hit the singularity along with the monkey and our rescue mission all of this describes a non-rotating uncharged black hole a swathes chair black hole even this simple case is a good deal more complicated than I let on for example I only showed you half of the Penrose diagram the complete mathematical solution for a swash shield black hole has two additional regions one corresponding to a parallel universe on the other side of an untrim hole the einstein-rosen bridge and down here we have what we call a white hole these are strange mathematical entities and probably aren't real but we'll certainly come back to them we'll also come back to what happens if we set the black hole speeding or add some electric charge then our Penrose diagram blooms outwards to include potentially infinite parallel