Skip to content

FloatHeadPhysics Physics

We were wrong about how time works inside a black hole! (My mind is blown)

Mahesh Shenoy of FloatHeadPhysics spent months with one great book on relativity, and he comes out the other side with a single tool that dissolves every paradox people repeat about black holes. The tool is a spacetime map that keeps light rays at exactly 45 degrees everywhere, inside and out. He does not derive it from Einstein's field equations.

Published Apr 24, 2026 45:25 video 26 min read Added Jun 14, 2026 Open on YouTube →

At a glance

Mahesh Shenoy of FloatHeadPhysics spent months with one great book on relativity, and he comes out the other side with a single tool that dissolves every paradox people repeat about black holes. The tool is a spacetime map that keeps light rays at exactly 45 degrees everywhere, inside and out. He does not derive it from Einstein's field equations. He rebuilds it from scratch out of one borrowed idea: a constantly accelerating observer in empty, gravity free space already has a horizon behind them, a Rindler horizon, and by the equivalence principle that flat space picture carries straight over to a real black hole.

With that map in hand he answers the questions that usually go unanswered honestly. Does Bob take infinite time to fall in? From Alice's perspective, genuinely yes, and yet that statement carries no physical meaning at all. Do black holes ever form, or evaporate before anything falls in? Same trick, same answer. Does Bob see the whole future of the universe rush past as he crosses? No. And the deepest payoff: past the event horizon the roles of space and time swap. Falling toward the singularity stops being a place you could steer away from and becomes a moment you cannot avoid, as unavoidable as next Saturday.

This is a rediscovery, not a recap of conclusions. The page below walks the same path Mahesh walks, in order, with every analogy, every objection he raises against himself, and the geometry that settles each one.

The setup: Bob jumps, and four questions that never get answered

Alice and Bob hover close to a non spinning black hole. Bob decides to jump in. From Bob's own point of view, no mystery, he falls in. The mystery is Alice. The story everybody repeats is that she watches him slow, redden, and freeze at the horizon, and the usual reassurance is that this is "just what she sees," that Bob really goes in and she simply cannot witness it.

Mahesh refuses to let that off the hook, because the standard objection is correct: time really does dilate near a black hole and stop at the horizon from Alice's perspective. So it should not be merely visual. It should mean Bob takes literally infinite time to enter. And if that is true, a chain of absurdities follows that nobody resolves cleanly:

If nothing ever crosses the horizon from outside, how does a black hole ever form, since the collapsing matter would also need infinite time to fall in?
Black holes evaporate in finite (if monstrous) time. So should a hole not evaporate out from under Bob before he ever reaches it?
And as Bob falls, does he see the entire future of the universe play out in fast forward behind him?

Mahesh is candid that he never got satisfying answers until now. The whole video is the rediscovery, deliberately pretending to know nothing about horizons and building the physics back up step by step so the answers are seen rather than asserted.

Can you outrun light? Rindler's deceptively simple question

The guide for the rediscovery is Wolfgang Rindler, the physicist who coined the term event horizon. He opens with what sounds like a trick: turn on a flashlight behind Alice, have her fire her engines and accelerate, and ask whether she can outrun the beam.

The naive answer is no. Alice is always slower than light, so the gap shrinks and the light always catches her eventually. The correct answer needs a spacetime diagram. Even an object at rest still moves through time, so its world line points straight up. Move at constant velocity and the world line tilts. Faster means more tilt, with light setting the maximum tilt. Choose convenient units (light years for distance, years for time) and that maximum is exactly 45 degrees. Every physical world line must stay inside that 45 degree wedge, the future light cone, and nothing reaches events outside it.

Now accelerate Alice. She starts vertical, then her line bends as her speed climbs, but relativity forbids her ever reaching c, so the bend only approaches 45 degrees, touching it at infinity. Her world line is a hyperbola whose asymptote is the 45 degree light line. Here is the punch: a flash starting anywhere ahead of that asymptote eventually reaches her, a flash starting exactly on it takes infinite time, and a flash starting behind it never reaches her at all. So a constantly accelerating Alice genuinely can outrun light, as long as that light started far enough back.

Figure 1. The Rindler horizon, with no gravity anywhere. Alice's acceleration bends her world line into a hyperbola that hugs the 45 degree light line. Flash A, ahead of that line, eventually catches her; flash B, starting behind it, never can. The asymptote is a one way membrane she creates simply by accelerating.

Rindler then sharpens it. It is not really about light. If Bob sits ahead of that 45 degree line, he can always catch Alice, because her world line lives in his future. The instant Bob crosses behind it, he can never reach her, because he can never escape that region himself. That is an event horizon, built in perfectly flat spacetime with no mass and no gravity in sight. Mahesh's reaction is the right one: holy smokes, this is starting to sound exactly like a black hole. Rindler's reply is one word: exactly. The mere act of accelerating leaves a patch of spacetime behind you whose signals can never reach you again. He calls it the horizon; we call it the Rindler horizon.

Why a "fake" horizon is the key to a real one

Mahesh pushes back, and his objection is good. This horizon only exists while Alice accelerates. Stop the engines and light from everywhere floods back in; the horizon vanishes. It feels fake. Why bother?

Because Alice is not alone. Draw a whole family of hyperbolas sharing that same 45 degree asymptote. They all share the same horizon. The wide ones, far from the horizon, need gentle acceleration; the tight ones, near it, need fierce acceleration. Look at that fleet of accelerating ships and it is indistinguishable from a crowd of observers hovering at different heights above a black hole, each firing engines harder the lower they sit.

That is the equivalence principle, stated by Rindler in Alice's own words: without looking outside, she and her friends cannot tell whether they are accelerating through empty space or hovering near a black hole. Both feel a gravity like pull that weakens with distance; both have a horizon behind them. Locally the physics is identical. Acceleration is indistinguishable from gravity. So the "fake" Rindler horizon is the smart way in. It is intuitive, it lives in flat spacetime where light is honestly at 45 degrees, and the equivalence principle ferries every conclusion across to a real curved black hole with none of the messy equations.

There is a snag, and Mahesh spots it. Near a real black hole, Alice and the horizon and her friends stay at fixed distances forever. But on the flat diagram the hyperbolas visibly crowd together as they climb. The two pictures look different. Resolving that snag requires understanding how each accelerating observer defines "now," which means confronting simultaneity.

Simultaneity: why "right now, far away" means nothing

Mahesh sets up the strangeness with aliens. Suppose an alien fleet, millions of light years off, launches its invasion of Earth. From his frame the invasion has begun. From his wife's frame, walking past him, it has not; for her the aliens are still in the planning meeting, and will not launch for months. The event cannot both have happened and not happened. Yet relativity says it does, for different observers.

The intuition pump is two cars. Mahesh drives straight and passes a rock; the rock is in his present, neither past nor future, right beside him. His wife drives at a slight angle, alongside him, but she has not reached the rock yet; for her it is in the future. Same rock, present for one driver and future for the other, because their headings differ. Their "lines of sight," the slices they each call now, are tilted relative to one another. They simply carve the road into different now slices.

Spacetime does exactly this. Relative motion tilts world lines, and so it tilts the lines of simultaneity, each observer's definition of now. His present slice and his wife's present slice are tipped against each other, so the alien launch can sit in his now and her future at once.

But Mahesh draws the crucial distinction. With the cars you can simply look sideways and confirm the rock; it is direct perception. In spacetime you cannot see what is happening far away right now, because seeing requires light to crawl to your eyes first. The simultaneity line is not about appearances. It is your statement about what is actually happening out there, now, in your reality. And relative motion can genuinely turn your present into someone else's future.

We never notice because the diagram is wildly exaggerated. Everyday relative speeds are a sliver of light speed, so everyone's now slices are nearly parallel and we agree on past, present, and future for anything close by. We then wrongly assume that agreement covers the whole universe. It does not; at millions of light years the tilt is enormous. This is what Einstein meant: "The distinction between past, present, and future is only a stubbornly persistent illusion." The moral, which Mahesh will lean on again and again, is that "what is happening right now far away" carries physical meaning only locally. Extended across great distances it is a bookkeeping choice, not a fact, because your now is someone's future.

Hyperbolic geometry: drawing Alice's "now"

To use any of this on Alice, Mahesh needs her simultaneity lines, and her world line is a curve, which sounds hard. The rescue is an analogy between spacetime and ordinary space that he clearly delights in.

In ordinary space, turning is circular. As a car rounds a circle, its line of sight (its now) sweeps around as a tangent to that circle, and the successive now lines all meet at the center. In spacetime, turning is hyperbolic. As a ship rides a hyperbolic world line, its simultaneity sweeps as a tangent to that hyperbola, and the successive now lines all converge on the hyperbola's vertex. Alice's world line is a hyperbola, so her now slices are a fan of lines radiating from the vertex.

And the analogy goes one step deeper. Every point on a circle is the same distance from the center. Every point on a hyperbola is the same proper distance from its vertex, in the hyperbolic sense. It does not look that way on paper, because flat paper cannot honestly draw hyperbolic geometry, but it is true.

Figure 2. The geometry Mahesh leans on. Circular motion sends radii to a center, with every rim point equidistant. Hyperbolic motion sends simultaneity lines to a vertex, with every point on the hyperbola the same proper distance away. Alice's now slices are this fan from the vertex, and that single fact freezes the light beam.

Now bring back the flashlight, vertical world line, beam at 45 degrees. By our outside slices the beam front creeps toward Alice. But by her slices, fanning from the vertex, the beam front sits at the same proper distance from her at every moment, because all points on her hyperbola are equidistant from the vertex. So in Alice's reality the beam never advances. It is frozen at a fixed distance behind her, for all time. There is the infinite time dilation at the horizon, derived from pure geometry, with not a single equation about clocks. And it applies to the whole family: each accelerating observer sees that beam frozen behind them. They do not see it frozen, since seeing needs light to arrive; their simultaneity says it is frozen. Reality, not appearance.

That settles the snag too. The situation really is locally identical to hovering near a black hole, so the same map serves the real thing. Zoom out, complete it, and you have a spacetime map of a black hole, built from a flashlight and a fleet of accelerating ships.

The map that keeps light at 45 degrees

A natural complaint arrives. If the hovering ships sit at fixed distances, at rest relative to each other, shouldn't their world lines be vertical rather than curved? You can draw them vertical. That is the familiar Schwarzschild diagram, and it feels more intuitive. The catch is fatal: solve Einstein's field equations in those coordinates and the paths of light come out curved, and worse, near the horizon it looks as though nothing can cross at all. That very picture is part of why Einstein and Eddington doubted black holes were real.

The fix is the same realization every cartographer makes. A spacetime diagram is a map, and every flat map of a curved thing distorts something. Flatten the curved Earth and you must sacrifice either angles or areas. The vertical world line map preserves the look of "hovering at rest" but mangles the light paths. So physicists asked for a different projection, one that preserves the 45 degree light cone everywhere. Finding it from the equations took serious work (this is the Kruskal type or Penrose style map). Mahesh got it for free, because he built it from the Rindler horizon, which lives in flat spacetime where light is honestly at 45 degrees, and the equivalence principle carried that 45 degree honesty into the curved case. No coordinate transformations, no mess. A map you can simply read.

Reading the map: Bob's fall, and what Alice "sees"

Drop Bob on the map and draw his future light cone. He has a future inside the horizon, so he can fall in, and a future outside it, so with rockets fired just right he could avoid it. Without rockets he free falls and crosses. As he descends, more and more of his future cone tips inside the horizon. Right up to the edge there is a shrinking window to fire and escape; the instant he crosses, the window is gone, because even a light speed dash cannot climb back out. Trapped, he transmits a last message, "Goodbye, universe," which is itself trapped inside and never emerges. On the map you simply see these events happen, in finite time on Bob's own clock. That is why we say Bob plainly enters and does things inside.

Now Alice. First, what she sees: draw 45 degree light rays leaving Bob at regular ticks of his clock. Early on Alice receives them on schedule; as Bob nears the horizon the gaps stretch, and the final ray, the one leaving exactly at the horizon, takes infinite time to reach her. So she literally sees him slow and freeze. The map gives this without a word about time dilation; it is just light paths.

Then the harder question: not what she sees, but what is, from her perspective. For that, her simultaneity lines. Label them t = 0, 1, 2, 3, and so on, with t = infinity being one particular 45 degree line. Walk them up and Bob, located by where each slice crosses his world line, really does slow, and on every finite slice he is still outside the horizon. The slice that finally reaches him crossing is the t = infinity line. So Alice must wait an infinite amount of time for Bob to cross. Not appearance. From her perspective Bob genuinely takes infinite time to enter.

Figure 3. The whole black hole on one honest map, light always at 45 degrees. Alice's now slices (gray) fan upward and only catch Bob's crossing at t = infinity, so by her clock his fall takes forever. Yet a single 45 degree ray back from his world line marks the real last chance to rescue him. After that point, his outside path is no longer in her future cone, even though her slices still place him "outside."

The ant on the table: existing without a "when"

So Rindler asks the sharpest question. From Alice's perspective, did Bob ever say "Goodbye, universe"? Surely not, since even reaching the horizon eats infinite time, so nothing beyond it could ever happen for her. Or does it?

Enter the ant. Put an ant on a table and lay down a normal grid; the ant sits at, say, x = 3, y = 2. Now lay a perverse grid where the lines bunch up forever, x = 1 here, x = 2 halfway to some limit, x = 3 halfway again, the lines crowding toward a wall that is x = infinity, with the ant beyond that wall. In this grid the ant has no coordinate at all; you could run x through every value to infinity and never reach it. Does the ant therefore not exist? Absurd. Of course it exists. Whether the ant is on the table has nothing to do with which grid you painted on the table.

That is the whole point. Bob, Alice, and everyone share one spacetime, and events on it either happen or they do not, objectively, independent of any coordinate grid. Bob's goodbye plainly happens, so it happens for everyone, including Alice, since she shares the same spacetime. These events exist; by definition they happen.

But then, when do they happen for Alice? Rindler's answer: never. Never in her timeline. The confusion finally cracks open. Everyday life offers only two boxes: either an event exists, and then it sits somewhere in your past, present, or future; or it is not in your timeline, and then it does not exist. Black holes force a third box. An event can exist, can genuinely happen, and still not lie anywhere in your past, present, or future. The events inside the horizon are exactly that. If someone had merely asserted this, Mahesh would have refused it. But here it is, drawn on the map: real events that share his spacetime, yet take no coordinate on Alice's grid because her map simply does not reach them.

The rescue test: why "infinite time" means nothing

One thread still resists: how can it take infinite time for Bob to enter and yet the crossing genuinely happens? Rindler's reply is the simultaneity lesson cashed in. "What is happening now far away" has no physical significance, so Alice's infinite wait carries no real meaning either.

Mahesh wants proof, not a slogan, and Rindler gives him an operational test. If you truly believe Bob is always outside the horizon from Alice's view, then the literal content of that claim is that Alice could go rescue him at any later time. So test it. Pick a point on Alice's world line and ask whether Bob's outside world line lies in her future light cone, the only events she can actually reach. Past a certain point on her path it does not. She cannot rescue him, even though her simultaneity still places him "outside." Draw the single 45 degree line that marks that point and it is the genuine last chance to save Bob. Before it she can reach him; after it she cannot, ever.

That convinced Mahesh, and it is convincing. If Bob were really always out there, rescue should always be possible. It is not. So "Bob is always outside" is the ant's missing coordinate, a feature of the grid, not the territory, and we should stop taking it literally.

Formation and evaporation: the same trick twice

The same map disposes of the two formation puzzles. Take a star before collapse. While it is stable its surface rides a hyperbola, just like hovering. Then it collapses, the surface falls inward, shrinks past its own Schwarzschild radius (the critical radius below which it becomes a black hole), and the horizon forms. Drop Bob in: he can hover and avoid it, hit the star, or free fall across. From Alice's simultaneity the horizon takes infinite time to form and the matter never reaches it, but that statement, again, carries no physical meaning. Bob can cross, and Alice herself can cross and check. The horizon is really there.

Evaporation is the same shape. Black holes evaporate in finite, monstrous, but finite time via Hawking radiation. Put the evaporation event somewhere up the map. Mahesh is honest that he does not know what the map does past that point; the horizon ends somehow. It does not matter. The horizon exists over the stretch Bob actually falls through, so Bob crosses and is inside, full stop. From Alice's perspective formation takes infinite time, Bob's entry takes infinite time, and even evaporation takes infinite time, and all of that means exactly nothing. Said once more, deliberately, as the moral of the whole story: thinking about what is happening now far away carries no physical meaning.

Inside: where space becomes time

Now the heart of it, and the part that earns the title. Why can Bob not hover inside, the way the outside ships hover? On the outside, each hyperbola is a fixed distance from the hole, so label them by a radius R: R = 1 the horizon, then 1.2, 1.4, the heights you can hold. To hover inside you would need another hyperbola with the same 45 degree asymptote opening to the right, and you cannot draw one. Physically, holding a fixed R closer in demands more acceleration, and right at the horizon it demands infinite acceleration, because the hyperbola has degenerated into the 45 degree V of light itself, which only light can ride. There is no hovering hyperbola past that. That is why you cannot hold position inside.

What you can draw inside is a family of hyperbolas opening upward, sharing the same asymptote. Those are the smaller values of R: one just inside, a smaller one below it, and finally the center as a hyperbola near the top. That is the map of the interior, and reading it is the revelation.

Figure 4. The swap, drawn. Outside the horizon the R hyperbolas open sideways and you may hold any R you like, the way you may stand still in space. Inside, the R hyperbolas open upward and every future world line marches to smaller R, the way every future marches to later times. R has become a clock. The center, R = 0, is not a place ahead of you but a moment you cannot dodge.

Outside, you can hold any R, drift to a higher one, or a lower one; all of it is in your future. That is what space is: free movement. Inside, you cannot hold an R. Your future lies only at smaller R, then smaller still, then the center, unavoidably. That is exactly how time works: you cannot hover at Tuesday, you slide to Wednesday whether you like it or not. So space behaves like time. This is the real meaning of "your future lies at the center." You cannot avoid the singularity any more than you can avoid next Saturday. That is why there is no hovering and no orbiting inside; whatever you do, you arrive at the center.

And the time coordinate does the mirror image. Outside you cannot hold a time coordinate, you are dragged from t = 1 to 2 to 3. Inside you can sit at one time coordinate or jump to another freely. So time behaves like space, space behaves like time. Asked what that physically means, Rindler is blunt: "Nothing. It's just coordinates. It doesn't mean anything." The coordinate labels are bookkeeping. The physical fact, the one that survives any relabeling, is that inside the horizon Bob's future points at the center, and nothing can turn it aside.

The center, and what we do not know

What happens at the center? Spacetime curvature, the Riemann curvature tensor, runs to infinity. Tidal forces run to infinity with it, which means spaghettification, anything reaching the center is stretched and shredded. At the quantum level we simply do not know what happens; that is why it is called a singularity and why it remains one of the open questions in physics today. Mahesh is content to leave it open rather than pretend.

Two myths cleared, and a door left ajar

Does Bob, glancing back as he falls, watch the entire future of the universe stream past in fast forward? Draw the 45 degree light signals reaching him from Alice and the answer is plainly no. There is a last signal from Alice he ever receives; beyond it, nothing from her or from the rest of the universe arrives before he hits the center. The popular image is wrong.

Finally, the heartbreak case. Suppose Alice has already passed her last rescue threshold and decides she would rather plunge in and meet Bob one final time before they fall to the center together. Can she always? No. Bob's world line ends at the center; draw the 45 degree line up from that endpoint and it marks the last moment Alice can still cross and reach him inside. Inside that window she falls in and they spend their remaining time together. Miss it and she can never meet him, even by jumping into the same hole. A genuinely sad geometry.

And the door left open: that far region of the map, and what changes for a rotating black hole. There, Mahesh teases, Bob could have a wholly different future, even emerge to meet a different Alice in a different universe. But that, he says, is a story for another day.

Key takeaways

A constantly accelerating observer in empty, gravity free space already has a horizon behind them, the Rindler horizon, and by the equivalence principle that flat space picture transfers exactly to a real black hole.
"What is happening right now far away" carries physical meaning only locally. Stretched across great distances, simultaneity is a coordinate choice, not a fact, because your present can be someone else's future.
Build a spacetime map that keeps light at 45 degrees everywhere and every black hole paradox becomes readable. The familiar vertical (Schwarzschild) map distorts light paths, which is part of why Einstein and Eddington doubted black holes.
From Alice's perspective Bob really does take infinite time to cross, and that statement carries no physical meaning, proven by the rescue test: after a finite threshold she cannot reach him, so "always outside" is the ant's missing coordinate, not reality.
Events can exist without belonging to any observer's past, present, or future. Black holes force a third category beyond "exists in my timeline" and "does not exist."
Formation, evaporation, and the infinite fall are the same illusion three times over; the horizon genuinely forms and Bob genuinely crosses.
Inside the horizon, space and time swap roles. You cannot hold a position any more than you can hold a moment, so reaching the singularity is unavoidable, like next Saturday. The singularity is a moment, not a place.
Bob does not see the universe's future in fast forward; there is a last signal he ever receives. At the center, curvature and tidal forces diverge, spaghettification follows, and the quantum behavior is unknown.

Chapters

Timestamps are clickable. Click one and the player jumps there and keeps playing while you read. This video has no creator set chapters, so these are estimated from position in the talk.

0:00 The setup: Bob jumps, and four unanswered questions
3:30 Rindler asks: can you outrun light?
7:30 The Rindler horizon in flat spacetime
8:40 Why a "fake" horizon is the key (the equivalence principle)
12:30 Simultaneity: the alien invasion and the two cars
18:00 Hyperbolic geometry and Alice's "now"
22:30 The frozen flashlight beam (infinite time dilation, from geometry)
25:00 Building the map that keeps light at 45 degrees
28:30 Reading the map: Bob's fall and what Alice sees
31:30 The ant on the table: existing without a "when"
35:00 The rescue test: why infinite time means nothing
37:30 Black hole formation and evaporation
40:00 Inside the horizon: space becomes time
43:00 The singularity, the fast forward myth, the last meeting, and rotating black holes

Notable quotes

Without looking outside, Alice and her friends have no way of telling whether they are accelerating in an empty patch of space or hovering near a black hole. Wolfgang Rindler, voiced by Mahesh, 8:00

The distinction between past, present, and future is only a stubbornly persistent illusion. Albert Einstein, quoted by Mahesh, 17:00

Whether the ant exists on the table or not does not depend upon what kind of grid you put on it. Mahesh Shenoy, 33:00

Bob, Alice, and everybody in this universe shares the exact same space-time. And events on that space-time either happens or it doesn't. It's not subjective. It's not relative. Mahesh Shenoy, 33:30

Never in her timeline. Wolfgang Rindler, voiced by Mahesh, 34:10

Your future lies at the center. You cannot avoid it, just like how you cannot avoid next Saturday. Mahesh Shenoy, 41:00

What does that physically mean, Rindler? Nothing. It's just coordinates. It doesn't mean anything. Mahesh Shenoy and Rindler, 42:00

Thinking about what's happening now far away carries no physical meaning. That, I think, is the moral of the story. Mahesh Shenoy, 39:30

Resources mentioned

Wolfgang Rindler, the relativist who coined "event horizon," and the Rindler horizon of an accelerating observer in flat spacetime.
Einstein's equivalence principle, that local acceleration and gravity are indistinguishable.
The relativity of simultaneity and the Minkowski spacetime diagram.
Einstein's field equations and the Schwarzschild coordinates whose distorted light paths made Einstein and Arthur Eddington doubt black holes, versus the Penrose and Kruskal style maps that keep light at 45 degrees.
The Schwarzschild radius, the event horizon, and the singularity.
The Riemann curvature tensor, the diverging tidal forces it measures, and spaghettification.
Hawking radiation and black hole evaporation, and the rotating black hole hinted at for a future video.
An unnamed but, in Mahesh's words, incredible book on relativity he read for months to crack this, plus the FloatHeadPhysics Patreon where he documents how he learns relativity.
boot.dev, the video's sponsor, a puzzle based platform for learning back end coding.

The one idea to walk away with

Strip the coordinates away and the black hole stops being paradoxical. Bob's "infinite" fall, the horizon that "never" forms, the evaporation that "never" finishes, all of it is the ant beyond the edge of a badly drawn grid. The events are real; only the timestamps are fiction. And once you cross the edge, the deepest fact reverses on you: the singularity is not a destination in space you might steer around, it is a moment in your future you cannot refuse. Inside a black hole, falling is no longer like moving. It is like waiting for Saturday.

Full transcript

Alice and Bob are hovering close to a non-spinning black hole, and Bob decides to jump in. What happens to him? You probably know from Bob's own perspective, he does enter the black hole. But the question is what happens from Alice's perspective? The most common story I hear is as Bob falls closer, Alice sees him slow down and eventually freeze at the horizon. But, and this is important, that's just what she sees. In reality, Bob actually goes in. She just can't see it. But wait a second. Doesn't time really slow down near a black hole and stop at the event horizon from Alice's perspective? So shouldn't it mean that it's not just what she sees, but he actually takes an infinite time to enter the hole? So from her perspective, nothing should ever enter a black hole, right? And if that is the case, how do black holes form in the first place because matter would take an infinite time to collapse. Or, shouldn't black holes evaporate even before Bob enters in? And would Bob actually see the entire universe in fast forward as he falls through? I never got a satisfactory answer for all these questions until now. For the past few months, I've been going through this incredible book on relativity, and my god, I think I've finally cracked it. So in this video, we're going to pretend we don't know anything about black holes or event horizons, and step by step rediscover the real physics behind them intuitively, answering every single burning question about event horizons. So if you're ready for this, let's begin. We start by talking to Wolfgang Rindler, the person who coined the term event horizon. And he asks a seemingly random question. "Mahesh, can you outrun light?" What do you mean? Here's our friend Alice and there's a flashlight behind her. As we turn on the flashlight, she blasts her ship and starts accelerating. The question is, with enough acceleration, can she outrun that beam of light or will the light eventually catch up to her? My immediate response is, "Rindler, that's an easy question. I mean, look, no matter how much Alice accelerates, she will always be slower than light. So the gap between them keeps shrinking and eventually, given enough time, light will always catch up." Or will it? Rindler reminds us that even if a shuttle is at rest in space, it is still moving through time. So in space-time, its world line is vertical. If it's moving at a constant velocity through space, its world line is slanted. The faster it moves, the more it tilts with the maximum tilt corresponding to that of light. Now, we will conveniently choose units like light-years for space and years for time or light-seconds and seconds. That way, this maximum angle always turns out to be 45 degrees. It's just nice. So this means all physical world lines must lie within this 45 degrees, meaning your entire future is restricted to this region, your future light cone. You simply cannot reach events outside it, ever. Anyways, since our friend Alice is accelerating, what does her world line look like? Well, when she's at rest, her world line starts vertically. Then she accelerates, so her velocity keeps increasing, meaning her world line gets curved. But remember, even if she were to accelerate forever, according to relativity, it would take her an infinite amount of time to reach the speed of light. This means her world line will curve closer and closer to that 45 degrees, but it will take an infinite amount of time to actually reach 45 degrees. In other words, it will get closer and closer to this 45 degree line, but it will only touch it at infinity. So the world line becomes a hyperbola with this 45 degree asymptote, meaning a line that touches it at infinity. But wait. A 45 degree line is also the world line of light. So this means if a flash of light were to start anywhere in this region, it will eventually reach her. But if it starts exactly here, that light would take an infinite amount of time to reach her. Which means if the flash starts anywhere behind this line, it would never reach her. So think about what this means. As long as she's constantly accelerating, even though she will never reach the speed of light, her speed will always be slower than that of light, she can outrun it, provided that light ray starts from far back enough. But Rindler says it's not just about light. It reveals something much deeper. If Bob, for example, was outside this region, he can always catch up with Alice because Alice's world line is part of his future. But once he enters this region, it'll be impossible for him to reach her because it'll be impossible for him to escape it. Holy smokes! This is beginning to sound like the event horizon of a black hole. But Rindler, that's crazy. This is flat space-time. There's no gravity, there's no mass anywhere. And Rindler says, "Exactly." Apparently, just the act of accelerating can leave behind a patch of space-time which cannot influence you anymore. Signals from there can never influence you. He calls that patch of space-time the horizon. And of course, we will call it the Rindler's horizon. I absolutely love it when we start with a seemingly simple question and then dig deeper and end up with something so profound. And that's exactly how you would learn back-end coding with boot.dev, the sponsor of this video. Their motto is pretty simple. Learn to code, but for real. But I think they mean it because if you use my link, you can actually get started for free without having to add your credit card details. And if you do have a look, you will see their course structure is pretty radical. For example, this Python course starts with a big goal of building a role-playing game. And each lesson, instead of just telling us things, starts with a curious puzzle. As we try to solve that puzzle, we end up rediscovering various insights about functions, loops, and whatnot. And you know I'm a sucker for rediscovery. And to top it off, coding is naturally hands-on. So you get immediate feedback. And if you do get stuck, there is an AI chatbot. But it doesn't just give us the answer directly. Instead, it nudges us in the right direction. And of course, they have gamified this whole thing with achievements and quests and experience points and levels and a lot of quirky MCQs as well. I've been a teacher for over a decade now, and I think this checks all my boxes for a pedagogically sound learning platform. But of course, why learn coding? I mean, for one, it allows you to build and automate and simulate almost anything. But a more concrete reason to learn back-end coding is that, look, back-end developers, come on, some of the highest median salaries in the US. And this is 2025 data, by the way. And if this sounds intriguing to you, don't take my word for it. Like I said, you can get started for free. Just follow the link in the description. And if you then think it's worth it to use my code floathead physics, you'll get 25% off for your first payment. All right, back to the video. Rindler's horizon sounds awesome, but I have a question. Rindler, this horizon only exists for Alice because she is accelerating, right? Yeah. And if she stops accelerating, light from everywhere can now reach her, and so the horizon disappears, right? Yes. Okay, this horizon is starting to sound pretty fake to me. Why are we even talking about it? Because Alice isn't the only one who experiences this particular horizon. We can draw a family of hyperbolic world lines, all sharing the same 45 degree asymptote, meaning they will all share the same horizon. Just that the world lines farther away are wider, meaning they need to maintain a lower acceleration, and the world lines closer need to maintain a higher acceleration. And I look at this and I'm like, oh my god, this is starting to look very similar to a bunch of observers hovering near a black hole. "Exactly," says Rindler. "Without looking outside, Alice and her friends have no way of telling whether they are accelerating in an empty patch of space or hovering near a black hole. In both cases, there is a horizon behind them. They experience a gravity-like force, which gets weaker with distance. So locally, the physics is identical. This is the Einstein's equivalence principle. Acceleration is indistinguishable from gravity." Which means even though Rindler horizons seem fake, they are pretty intuitive. And more importantly, the physics carries over to real black holes in curved space-time, which is anything but intuitive. This is the strategy. This is how we can rediscover the entire physics of black holes without having to touch messy equations. Rindler, you beauty. Take a bow. But wait. There is a problem. If they were all hovering near a real black hole, then Alice, the event horizon, and all her friends would be at fixed distances from each other, right? Yeah. But Rindler, look. Here we can clearly see the horizon and all her friends are getting closer and closer to each other. So I'm sorry Rindler, the two situations are clearly not identical. Or are they? See, from our inertial perspective, Rindler says, I'm absolutely right. They're all getting closer to each other. But what's happening to the distances from their perspective? That's important because it's their horizon. Well, isn't it the same? "No," says Rindler. To answer this question, we need to understand how their simultaneity works. Wait. What's simultaneity? Somewhere millions of light-years away, aliens could have started their invasion to Earth. But what's crazy is that even though that invasion has started from my perspective, from the perspective of my wife, who's just walking right here, it wouldn't have. For her, that invasion would only happen a few months later. For her, probably they're still discussing right now. That sounds crazy. The invasion should either start or not. How can both be true? Well, there's a surprisingly intuitive way to think about it. It's kind of like driving and coming across this rock. Right now, I'm just passing that rock. It's right next to me. So it's in my present. Not the past, not the future, but the present. But if my wife were driving at a slight angle, she would be right next to me. But look, she wouldn't have passed that rock yet. It's yet to happen. It's in her future. So how can the rock be both in the future and the present at the same time? Well, since we are moving at an angle, our lines of sight, which defines our now, are tilted with respect to each other. We are basically considering different slices of the space as now. That's what's happening over here, right? Now, guess what? The exact same thing happens in space-time. Because of relative motion, our worldlines are tilted with respect to each other. And that means our definitions of now, what we call the lines of simultaneity, are also tilted with respect to each other. So look, my present slice of space-time is tilted with respect to my wife's. So the alien invasion could have started right now for me. It's in my present. But for my wife, it's yet to happen. For her right now, they're probably still discussing it. So the situation is analogous to two cars. But there is an important difference. When it comes to the cars, I can just look besides me and say, "Aha, there's that rock. I am passing it right now." And of course, my wife would look at her side and say, "Aha, I see no rock over here. That rock is ahead of me. I'm yet to pass it." So we can both confirm what our present is and our future is. We can see it literally. But when it comes to space-time, we can't see what's happening right now far away because for that, light needs to reach our eyes. So when you extend your simultaneity lines far away, it's not about appearances, it is about your reality. It tells you what really is happening from your perspective far away. Relative motion can truly make my present my wife's future. But why don't we notice this in our everyday life? Well, because this picture is highly exaggerated. Our everyday speeds, relative speeds, are much, much, much, much slower than the speed of light. Which means our worldlines are almost parallel, making our simultaneity also almost parallel. And so for events close by, we pretty much agree on what's present, past, and future. And we tend to think this extends to the entire universe, but it doesn't. If you start looking at events millions of light-years away, the differences begin to show up. This is probably why Einstein said, and I quote, "The distinction between past, present, and future is only a stubbornly persistent illusion." So the mind-boggling takeaway here is the idea of what's happening right now only carries physical meaning locally. Only then will most agree on past, present, and future. But if you extend the idea of simultaneity far away, it's necessary to do that to build space-time maps, and we'll do it. But if you extend that and you start thinking about what's happening right now far away, well, it wouldn't have any physical meaning because my present can be someone's future. Anyways, coming back. This means drawing Alice's simultaneity is the key to understand what's happening from her perspective. But how do we do that? I mean, her worldline is curved, so it sounds pretty complex. The spacetime geometry is definitely non-intuitive. But what helps me is that it's incredibly analogous to regular space geometry. Here's what I mean. If we go back to the car analogy, in regular space, rotations are circular, right? So look, the lines of sight, the simultaneities, change as a tangent to the circle. But in spacetime, rotations are hyperbolic. So the simultaneity here will change as a tangent to the hyperbola. See? Analogous, right? But there's more. When a car goes in a circle, the simultaneities drawn at every moment meet at the center, right? Similarly, if a spacecraft takes a hyperbolic path in spacetime, the simultaneity lines all meet up at the vertex. But wait, we already know Alice's worldline is hyperbolic. So this is what her simultaneity slices look like. They all meet at the vertex. And if this isn't beautiful enough, get this. Just like how all points on circle are equidistant from the center, all points on a hyperbola are at the same proper distance from its vertex. Now, it doesn't look like that because we can't draw hyperbolic geometry, but the situation is analogous. Gosh, tell me this isn't beautiful. So coming back, we now have Alice's spacetime map, how she slices her spacetime every moment. But what exactly does this mean? Well, if we bring back the flashlight, its world line would be vertical because it's at rest with respect to us, and the light would be, of course, at 45 degrees. So according to our lines of simultaneity, the front of the beam comes closer and closer to her. But according to her, at this moment, the front of the beam is here. But a little later, at this moment, it's still there. At the same distance behind. Wait, it doesn't look like it's at the same distance, but remember, all distances from the vertex to the hyperbola are the same from her. Which means, no matter how much time passes, for her, that beam of light doesn't progress at all. For her, it's frozen there in time at a fixed location behind her. Ooh. You can begin to see the whole infinite time dilation at the horizon where it comes from. Oh my god, this is incredible. And of course, the exact same analysis applies to the entire family. That light beam is frozen in time at a fixed distance behind each one of them. Again, Rindler reminds us they don't see the light beam frozen because, remember, seeing requires light to reach your eyes. Simultaneity doesn't tell you what you see. Your simultaneity lines tell you what's happening right now far away. So this is not about appearances. This is about their reality. From their perspective, that beam of light is just frozen there at a fixed distance behind them. So indeed, the situation is locally indistinguishable from hovering close to a real black hole. So this means we can use the same physics, the same space-time map that we have discovered for the event horizon of a real black hole. So all we have to do now is zoom out and complete the map. There it is. Isn't it beautiful? But of course, I have a lot of questions. First of all, here each shuttle is now hovering at a fixed distance, right? Meaning they're all at rest with respect to each other, right? Yeah. So a part of me is wondering, shouldn't their world lines be vertical? So why does it look curved? Why isn't their world line vertical? Rindler says, we could have drawn them vertically like this. And I immediately look at this and say, "Hey, this feels so much more intuitive. Then why aren't we drawing it this way?" Well, because if you actually solve Einstein's field equations, then in this particular space-time diagram, you'll find that the path of light is curved. And in fact, look, it looks like nothing can even enter the event horizon. That led people like Einstein and Eddington to believe black holes might not even exist. But of course, eventually we realized that what we're looking at is just a map. And just like how every flat map of curved Earth is distorted, maybe every space-time map that we draw of a curved space-time is also distorted. Some maps preserve correct angles, but distort sizes massively. And others preserve sizes, but they distort angles. So this map of space-time preserves vertical world lines, but the paths of the light gets distorted. So physicists started wondering if they could somehow build a new map of space-time where the 45 degree light path could be preserved. And that required a lot of math, but we eventually found it. And guess what? That's the map that we have found it. But we did it way more intuitively. I mean, in this map, the world lines of the light is always at 45 degrees. How do we know? Well, because we built it from Rindler horizon, remember? And Rindler horizon comes from flat space-time where light travels at 45 degrees. Since we used the equivalence principle and translated that into our curved space-time, in our map, the 45 degree got preserved. So this was the reason why we did it all this way. This allowed us to sidestep the whole equations and coordinate transformations, all the messy math, and intuitively build a map. And now that we have it, we can use this as a tool to answer all our burning questions. All right, let's say Alice is hovering over here. So this is her world line. And let's say she drops Bob somewhere over here. What's going to happen to Bob? To answer that question, we draw Bob's future light cone. And we can immediately see Bob has a future inside the event horizon. So he can enter the black hole, which you can immediately see from here. But Bob also has a future over here, which means he can avoid the event horizon as long as he uses his rockets and, you know, fires it at the right amount, he can definitely avoid the event horizon. So that makes sense. But of course, since Bob doesn't have a rocket, let's assume that he takes a path something like this. This is a free fall path, and he enters the horizon. We'll talk about what happens inside a little bit later, says Rindler, but now the big question is, from Bob's perspective, how do things look like? Well, as he follows along this path, notice more and more of his future now lies inside the horizon. You can clearly see that. Now, just before reaching the horizon, if he changes his mind, and if he had fire, you know, if he had rockets, again, look, there is a small window that he can exit. But once he enters the horizon, that's it. You can clearly see there is no escape because even if he travels at the speed of light, he cannot escape. He's now trapped. But let's say he realizes there's no way back, and he sends one last transmission message. He says, "Goodbye, universe." Of course, even that message will never come out because it'll also be trapped inside the black hole. But from this, we can immediately see that these events happen for Bob. And now we understand why we say from Bob's perspective, he does enter the horizon. We can clearly see he enters the horizon in finite time in his clock, and he can do stuff inside the horizon. But now comes the big question. What is the story from Alice's perspective? Okay. First, let's think about what she sees. All we have to do is draw 45 degree line at periodic intervals. Here it goes. And now, notice when Alice is somewhere over here, she gets the signals pretty periodically, but as time goes on, notice the delay increases and eventually the last signal takes an infinite time for her to reach over there. Which means indeed she sees him slow down. The best thing about this picture, I don't have to talk about time dilation anymore. I can draw the path of light and I can talk about what she sees. Now comes the main question. What happens from her perspective? Not just what she sees, but what actually happens from her perspective. For that, we have to use her lines of simultaneity. So each line of simultaneity represents a moment in Alice's perspective. So let's call this as t equals 0, t equals 1, 2, 3, 4, 5, and t equals infinity would be somewhere over here. So at t equals 0, she's over here and from her perspective Bob is over here. Remember, she doesn't see Bob over there, but this is where Bob is from her perspective. Okay. At one, a little later, Bob is over here. A little later, Bob is over here. Woo! Woo! You can begin to see that Bob actually does slow down. Notice, he's slowing down from Alice's perspective. This is not about appearances. From her perspective, Bob will always be outside the horizon. Remember, this particular 45 degree line represents the infinite time, which means Alice actually has to wait an infinite amount of time for Bob to enter the horizon. So even that story is true. It's not just about appearances. Bob really takes an infinite amount of time to enter the horizon from Alice's perspective. So Rindler asks the most important question. From Alice's perspective, did Bob ever say goodbye universe? Well, my immediate response is no. Because from Alice's perspective, it already takes an infinite amount of time to just enter the horizon. So clearly nothing ever can happen beyond the horizon. So no. Nothing ever happens beyond the horizon from Alice's perspective. Or does it? Here's a table and there's an ant. What's the coordinate of this ant right now? And I say, well, for that we need a grid. Okay, let's put a grid. What's the coordinate right now? Okay, it's um x equals 3 and y equals 2. What if we change the grid? What if we use a different kind of coordinate system in which the x equals 1 line is over here? The next line x equals 2 is halfway in between. And x equals 3 would be halfway in between this. And x equals 4 would be here, x equals 5 would be here, and so on and so forth and so forth. And eventually x equals infinity will be somewhere over here. Okay. Now, according to this coordinate system, what's the coordinate of this ant? Well, I say we can't assign a coordinate anymore. So Rindler asks, does that mean the ant does not exist according to this system? And I say, that's absurd. Of course the ant exists. And Rindler says, no, no, no, no. I mean, think about it. Even if I go through infinite values of x, I can't reach the ant. So, obviously that ant does not exist as far as this coordinate system is concerned, right? And I say, come on, Rindler, what are you talking about? Whether the ant exists on the table or not does not depend upon what kind of grid you put on it. And that's exactly the point. If we go back over here, Bob, Alice, and everybody in this universe shares the exact same space-time. And events on that space-time either happens or it doesn't. It's not subjective. It's not relative. And it's independent of the coordinate system that you put on it. Now, clearly we can see that this event of Bob saying goodbye happens. And so, it happens for everybody. It happens for Bob. It happens for Alice as well because she also shares the same space-time. So if you think of it that way, these events exist. And so, by definition, they happen. So Bob does enter the horizon. Bob does say goodbye. And everything that Bob does inside happen even from Alice's perspective because they exist from Alice's perspective. But wait, Rindler. If that event happens, when does it happen according to Alice? And Rindler says, "Never." What? Never in her timeline. Okay. Oh, ho. Okay. I think I finally understand the source of all the confusion. Hear me out, okay? In everyday life, we have only two choices. Either an event exists, and when it does, it's always a part of our past, present, or future. We can always talk about when it happens, okay? And in case it's not a part of our timeline, then those events never happen. They don't exist at all. This is what we have intuition for. This is all that we usually experience in everyday life. But black holes force us to accept a third possibility. It's possible for events to exist but not be a part of our past, present, or future. It's possible for event to happen but not be a part of our timeline. And these are all the events inside the horizon. Now, if somebody had just told me this, I wouldn't have accepted it. I mean like it sounds cool, but come on. But now we are seeing it right in front of our eyes. These events exist because we all share same space-time. It exists for everyone. And yet we cannot assign a coordinate to it because Alice's map doesn't extend to it. But wait. I still can't reconcile this with the fact that it takes an infinite amount of time for Bob to enter the horizon. I mean, that's what the map tells us, right? Alice literally has to take an infinite amount. So how can I reconcile with the fact that events do happen? Like I'm not able to put it all together. And Rindler says, "Actually, Mahesh, it's quite easy. Remember what we learn about simultaneity. The idea of what's happening now far away has no physical significance. Which means even though from Alice's perspective it takes infinite time for Bob to enter the horizon, it carries no real meaning." Okay, I find that hard to accept. And Rindler says, "All right. Suppose you truly believe that Bob will never enter the horizon, that Bob is always outside the horizon as far as Alice is concerned. Then that would also mean that we can go and rescue Bob anytime in the future. Right? Like that's the literal meaning of that statement. He's always outside the horizon." And I say, "Yeah, that makes sense." Rindler says, "Let's test it out. Let's see if Alice can always save Bob anytime in the future because he's always outside the horizon." So let's go back over here. How do we check this? Well, let's say Alice is over here. Can she save Bob now from entering the horizon? To answer that question, all we have to make sure is whether Bob's worldline outside the horizon intersects with Alice's future. Is it a part of Alice's future light cone? So let's just concentrate on this worldline and let's look at Alice's future light cone and we immediately see, "Nope. This is not a part of her future, so she cannot rescue Bob anymore." Even though her simultaneity tells her that Bob is outside, she can't rescue him. In fact, we cannot draw a 45 degree line from here and realize that this is the threshold. As long as Alice is past this particular point, she can never save him. But if Alice is below that threshold, then look, she can save him because she can reach to him before he enters the horizon. So this really represents the last chance to rescue Bob. This totally convinced me. I mean, if Bob was truly out there, always, then we should have been able to rescue him always. But notice, we can't. So that clearly tells me and I'm able to accept it that that carries no physical meaning. So we should stop taking it literally. I love this map. Okay. On to some other confusing questions. If things take infinite time to enter the horizon, how does a black hole form in the first place? Shouldn't all the material be stuck near the horizon forever? Well, again, let's go back to the map. Let's say we have a star. Let's think about that star before it forms a black hole. Now, if that star is stable, then the surface also is also the world line of that surface is also a hyperbola. It's very similar to hovering. And now let's say that here is where it starts collapsing. Then it starts going inwards, and then eventually it becomes smaller than its own Schwarzschild radius, the critical radius below which it starts becoming a black hole, and that's where it becomes, and then the event horizon is formed. And again, if we drop Bob somewhere over here, we can clearly see what are the Bob's options? He can always avoid the whole thing and just, you know, hover. He can go and hit that star over here, but if he takes a path like this, he will enter the horizon. Again, from Alice's perspective, if you look at her simultaneity lines, it says the event horizon takes an infinite amount of time to form. That all the stuff is always out there. It never reaches the horizon. The horizon never forms according to her, but that statement carries no physical meaning, because remember what's happening right now far away carries no physical meaning. So if she drops Bob, Bob can certainly enter the horizon, and she too can certainly enter the horizon and check for herself. The horizon will exist. What about black hole evaporation? Because another confusion we have is if it takes infinite amount of time for Bob to fall through the horizon, and we know according to our current models that black holes can evaporate in finite time, horrendous amount of finite time, but nevertheless finite amount of time, shouldn't the black hole evaporate before Bob enters? Let's see. Suppose the black hole evaporation event happens somewhere over here. Now, honestly, I have no idea what's going to happen beyond this point to the map. The horizon disappears, or it goes away, but it doesn't matter because, look, the horizon exists from here to here, and Bob can certainly enter the horizon. So if Bob took this trajectory, then Bob would have entered the horizon, he would be inside the black hole. But, again, from Alice's perspective, it takes an infinite time for the horizon to form, it takes an infinite time for Bob to enter, it takes an infinite time for black hole to even evaporate. What does it mean? Nothing. Events far... I think you get it. But I'm going to say it one more time. Thinking about what's happening now far away carries no physical meaning. That, I think, is the moral of the story over here. What really happens to Bob inside the horizon? Why can't he hover there? Or why can't he orbit the center like we can do outside? We know he can't do that because we've heard of these stories, but can the map help us understand that? All right, let's do that, says Rindler. We now need to map the insides. How do we do that? Here's the way to think about it. If you look on the outside, each hyperbola represents a fixed distance from the black hole, right? So we can give each hyperbola an R coordinate. So the R equals 1, let's say, represents the event horizon. 1.2, 1.4, these are different distances at which you can hover. Now, the question is, can you hover inside the event horizon? To do that, I need to draw another hyperbola with the same asymptote, 45 degree line. And notice, I can't do that. Physically, this makes sense because as I go closer, my acceleration needs to increase to maintain this hyperbola, and eventually when I reach the event horizon, the acceleration needs to be infinite because the hyperbola converts into a 45 degree V, and that is the world line of light, and that takes an infinite acceleration if you want to maintain that. Beyond that, you cannot think about a hyperbola with the same asymptote opening to the right. That's why you can't hover. But we can draw a family of hyperbolae inside opening upwards. So I can draw a hyperbola that looks like this. So geometrically speaking, once I go inside, the lower values of R must look like this. Because, remember, the idea is straightforward. We draw hyperbolae that have the same asymptote. And so this is what a lower value of R would look like. An even lower would look like this, and eventually the center would look somewhat like this. And so this is the map of the inside of the black hole. So now let's look at what happens when you go inside. Notice that inside, your future lies towards the lower values of R. Meaning, wherever you go, it's impossible now to avoid these different values of R compared to what happens outside. Outside, you can stick to a particular hyperbola over here. You can hover over there. You can stick to a value of R and you can stay. If you choose, you can go here, or if you choose, you can go here. All of that is a part of your future. That's how space works. You're free to move anywhere you want. But notice inside, you are no longer free to move any values of R. You have to go to this R, and then after that, you have to go to this R, and then eventually, you hit the center. It's unavoidable. So in that sense, space behaves like time. Oh, this is why we say space behaves like time. This is why we say your future lies at the center. You cannot avoid it, just like how you cannot avoid next Saturday. That's what's happening, and that's why you cannot hover, you cannot orbit. Whatever you do, you have to reach the center. But what happens as something reaches the center of the black hole? Well, turns out that the curvature tends to go to infinity. It's technically called the Riemann curvature tensor that goes to infinity. Tidal forces, that means go to infinity, and that will certainly spaghettify anything and shred it apart. But what happens at a quantum level? If you had a quantum object that went towards the center, we don't know what happens. And the center is called the singularity because you have infinity over there, and we don't know what would happen at a quantum level. So that's an unknown. That's an open question for physics as of today. However, what about the time coordinates? Now, we can draw time coordinates just like we drew over here. And notice, time coordinates behave the opposite way. Outside, if you look at the time coordinates, you have no choice but to go from time t equals 1 to 2, and then from 2 to 3. You cannot hover at a particular time coordinate. That's not allowed. You have to go, you cannot avoid your future. But look inside, you can stick to a particular time coordinate, or you can jump to another time coordinate, or you can jump to this time coordinate. So in that sense, time behaves like space, space behaves like time. What does that physically mean, Rindler? Rindler says, "Nothing. It's just coordinates. It doesn't mean anything." What's more important is that for Bob, the future lies towards the center. If Bob were to look back as he falls through, would he see the entire future of the universe in fast-forward motion? Let's go back to the map. Let's just focus on how Bob sees Alice as he falls through. For that, we just have to draw 45 degree light signals from Alice all the way over here, and then we do that, we notice he does not see the entire future of Alice. In fact, if you can clearly see over here, this is the last signal he will ever get from Alice. Beyond that, he doesn't receive any signal, and same will be the case for the rest of the universe, which means no, he does not see the entire future of the universe in fast-forward motion. Last scenario. So we already know that there is a threshold beyond which Alice cannot save Bob. And let's say Alice has crossed that threshold, as you can see right now. And Alice realizes she loves Bob. She cannot live without him. So she would rather plunge into the black hole herself and meet up with Bob one last time before moving towards singularity together. So can she always do that, or is there a window for that as well? Again, we can go back to our map. Let's say Bob's world line ends over here. It cannot continue beyond that because this is the center. And so we can now draw a 45 degree line from here, and now this would represent the last chance to even meet Bob. So if she is somewhere between here, and if she decides to plunge into the black hole inside the horizon, she can meet up with Bob and be together for the rest of their lives. But if she misses that window, she will never be able to meet him even inside the black hole. And that would really be a sad story. But of course, our final question could be what does this part represent? And what if this was a rotating black hole? Well, then Bob could have a completely different future, an exciting future altogether. In fact, he could even meet a different Alice in a different universe altogether. But that's a story for another day. See you.