The video explores the fascinating realm of black holes, fundamental objects predicted by the General theory of relativity. It highlights how these enigmatic entities, which initially seemed preposterous, arise from the solutions to Einstein's field equations. These equations reveal the Curvature of spacetime around massive objects, resulting in phenomena such as the event horizon, where time appears to stand still to an outside observer. The discussion further touches upon the concepts of white holes and wormholes, offering theoretical insights into the possibility of parallel universes and alternate realms.

The video connects historical discoveries, starting with Newton's gravity theories and moving towards Einstein's revolutionary insights about spacetime. It shares the challenges and breakthroughs in physics that led to our current understanding of cosmic phenomena. Highlights include the role of physicists like Karl Schwarzschild in deriving solutions that predict black holes and how subsequent figures like Oppenheimer expanded the comprehension of stellar collapses leading to such singularities. Further, it interprets how these concepts have evolved and led to debates on the existence of white holes and the viability of Einstein-Rosen bridges as traversable paths between universes.

Key takeaways from the video:

Please remember to turn on the CC button to view the subtitles.

Key Vocabularies and Common Phrases:

1. Nemesis [ˈnɛməsɪs] - (n.) - A long-standing rival or archenemy.

Imagine you trap your Nemesis in a rocket ship and blast him off towards a black hole.

2. Event Horizon [ɪˌvɛnt həˈraɪzən] - (n.) - The boundary around a black hole beyond which nothing can escape.

...the instant when he should cross the event horizon, the point beyond which not even light can escape.

3. Redshifted [ˈrɛdˌʃɪftəd] - (adj.) - A phenomenon where the wavelength of light is stretched, making the light appear redder.

The light from the spaceship gets dimmer and redder until it completely fades from view.

4. Singularity [ˌsɪŋɡjʊˈlærɪti] - (n.) - A point in spacetime where gravitational forces cause matter to have infinite density and zero volume.

Shortly after Schwarzschild's solution was published, people noticed two problem spots at the center of the mass at r zero.

5. Degeneracy pressure [dɪˈʤɛnərəsi ˈprɛʃər] - (n.) - The pressure exerted by a system of fermions that arises when particles are forced into close proximity.

...realized that electron Degeneracy pressure has its limits.

6. Ergosphe [ˈɜrgəˌsfɪr] - (n.) - A region outside the event horizon of a rotating black hole where objects cannot remain in place.

Space gets dragged around...until it goes around faster than the speed of light. You've now entered into the first new the Ergosphere.

7. Hawking Radiation [ˈhɔkɪŋ ˌreɪdiˈeɪʃən] - (n.) - Theoretical radiation predicted to be emitted by black holes due to quantum effects.

Not directly mentioned in this content but related to the concepts discussed.

8. Special Relativity [ˈspeʃəl rɛləˈtɪvɪti] - (n.) - The theory of gravitation developed by Albert Einstein, expanding the theory of relativity to include the speed of light as constant.

... Einstein's decade of hard work after special relativity...

9. Schwarzschild radius [ˈʃvɔːrtʃʃɪld ˈreɪdiəs] - (n.) - The radius defining the event horizon of a black hole.

But there's another problem spot outside of it at a special distance from the center known as the Schwarzschild radius.

10. Parallel Universe [ˈpærəˌlɛl ˈjunɪˌvɜrs] - (n.) - A hypothetical self-contained separate reality coexisting with one's own.

It also implied the existence of parallel universes and even possibly a way to travel between them.

Exploring Black Holes White Holes, and Endless Universes

You can never see anything enter a black hole. Imagine you trap your Nemesis in a rocket ship and blast him off towards a black hole. He looks back at you, shaking his fist at a constant rate. As he zooms in, gravity gets stronger, so you would expect him to speed up. But that is not what you see. Instead, the rocket ship appears to be slowing down. Not only that, he also appears to be shaking his fist slower and slower. That's because, from your perspective, his time is slowing down at the very instant when he should cross the event horizon, the point beyond which not even light can escape.

He and his rocket ship do not disappear. Instead, they seem to stop, frozen in time. The light from the spaceship gets dimmer and redder until it completely fades from view. This is how any object would look crossing the event horizon. Light is still coming from the point where he crossed. It's just too redshifted to see. But if you could see that light, then in theory, you would see everything that has ever fallen into the black hole frozen on its horizon, including the star that formed it. But in practice, photons are emitted at discrete intervals, so there will be a last photon emitted outside the horizon, and therefore, these images will fade after some time.

This is just one of the strange results that comes out of the General theory of relativity, our current best theory of gravity. The first solution of Einstein's equations, predicted not only black holes, but also their opposite, white holes. It also implied the existence of parallel universes and even possibly a way to travel between them.

This is a video about the real science of black holes, white holes, and wormholes. The General theory of relativity arose, at least in part due to a fundamental flaw in newtonian gravity. In the 16 hundreds, Isaac Newton contemplated how an apple falls to the ground, how the moon orbits the earth and earth orbits the sun. And he concluded that every object with mass must attract every other. But Newton was troubled by his own theory.

How could masses separated by such vast distances apply a force on each other? He wrote that one body may act upon another at a distance through a vacuum, without the mediation of anything else, is to me so great an absurdity that I believe no man who has a competent faculty of thinking could ever fall into it.

One man who definitely had a competent faculty of thinking was Albert Einstein. And over 200 years later, he figured out how gravity is mediated. Bodies do not exert forces on each other directly. Instead, a mass like the sun curves the spacetime in its immediate vicinity. This then curves the spacetime around it, and so on, all the way to the earth. So the Earth orbits the sun. Because the spacetime Earth is passing through is curved.

Masses are affected by the local Curvature of spacetime, so no action at a distance is required. Mathematically, this is described by Einstein's field equations. Can you write down the Einstein field equation? This was the result of Einstein's decade of hard work after special relativity, and essentially what we've got in the field equations.

On one side it says, tell me about the distribution of matter and energy. The other side tells you what the resultant curvature of space time is from that distribution of matter and energy. And it's a single line. It looks like, oh, this is a simple equation, right? But it's not really one equation. It's a family of equations. And to make life more difficult, they are coupled equations, so they depend upon each other, and they are differential equations. So it means that there are integrals that have to be done. Da da da.

So there's a whole bunch of steps that you need to do to solve the field equations. To see what a solution to these equations would look like, we need a tool to understand spacetime. So, imagine you're floating around in empty space. A flash of light goes off above your head and spreads out out in all directions. Now, your entire future, anything that can and will ever happen to you will occur within this bubble, because the only way to get out of it would be to travel faster than light in two dimensions.

This bubble is just a growing circle. If we allow time to run up the screen and take snapshots at regular intervals, then this light bubble traces out a cone, your future light cone. By convention, the axes are scaled so that light rays always travel at 45 degrees. This cone reveals the only region of spacetime that you can ever hope to explore and influence.

Now, imagine that instead of a flash of light above your head, those photons were actually traveling in from all corners of the universe, and they met at that instant and then continued traveling on in their separate directions. Well, in that case, then into the past. These photons also reveal a light cone, your past light cone. Only events that happened inside this cone could have affected you up to the present moment. We can simplify this diagram even further by plotting just one spatial and one time dimension. This is the spacetime diagram of empty space.

If you want to measure how far apart two events are in spacetime, you use something called the spacetime interval. The interval squared is equal to minus dt squared plus dx squared. Since spacetime is flat, the geometry is the same everywhere. And so this formula holds throughout the entire diagram, which makes it really easy to measure the separation between any two events.

But around a mass, spacetime is curved, and therefore you need to modify the equation to take into account the geometry. This is what solutions to Einstein's equations are like. They tell you how spacetime curves and how to measure the separation between two events in that curved geometry.

Einstein published his equations in 1915 during the First World War, but he couldnt find an exact solution. Luckily, a copy of his paper made its way to the eastern front, where Germany was fighting Russia. Stationed there was one of the best astrophysicists of the time, Karl Schwarzschild. Despite being 41 years old, he had volunteered to calculate artillery trajectories for the german army, at least until a greater challenge caught his attention.

How to solve Einstein's field equations. Schwarzschild did the standard physicist thing and imagined the simplest possible scenario, an eternal static universe with nothing in it except a single spherically symmetric point mass. This mass was electrically neutral and not rotating. Since this was the only feature of his universe, he measured everything using spherical coordinates relative to the center of this mass. So r is the radius, and theta and phi give the angles.

For his time coordinate. He chose time as being measured by someone far away from the mass, where spacetime is essentially flat. Using this approach, Schwarzschild found the first non trivial solution to Einsteins equations, which nowadays we write like this. This Schwarzschild metric describes how spacetime curves outside of the mass. Its pretty simple and makes intuitive sense.

Far away from the mass, spacetime is nearly flat. But as you get closer and closer to it, spacetime becomes more and more curved. It attracts objects in and time runs slower. Schwarzschild sent his solution to Einstein, concluding with the war treated me kindly enough, in spite of the heavy gunfire to allow me to get away from it all and take this walk in the land of your ideas.

Einstein replied, I have read your paper with the utmost interest. I had not expected that one could formulate the exact solution to the problem in such a simple way. But what seemed at first quite simple soon became more complicated. Shortly after Schwarzschild's solution was published, people noticed two problem spots at the center of the mass at r zero.

This term is divided by zero, so it blows up to infinity, and therefore this equation breaks down and it can no longer describe what's physically happening. This is what's called a Singularity. Maybe that point could be excused because it's in the middle of the mass. But there's another problem spot outside of it at a special distance from the center known as the Schwarzschild radius.

This term blows up. So there is a second Singularity. What is going on here? Well, at the Schwarzschild radius, the spacetime curvature becomes so steep that the escape velocity, the speed that anything would need to leave there, is the speed of light. And that would mean that inside the Schwarzschild radius, nothing, not even light, would be able to escape.

So you'd have this dark object that swallows up matter and lightning, a black hole, if you will. But most scientists doubted that such an object could exist because it would require a lot of mass to collapse down into a tiny space. How could that possibly ever happen? Astronomers at the time were studying what happens at the end of a star's life.

During its lifetime, the inward force of gravity is balanced by the outward radiation pressure created by the energy released through nuclear fusion. But when the fuel runs out, the radiation pressure drops. So gravity pulls all the star material inwards. But how far? Most astronomers believed some physical process would hold it up. And in 1926, Ralph Fowler came up with a possible mechanism.

Paoli's exclusion principle states that fermions, like electrons, cannot occupy the same state. So as matter gets pushed closer and closer together, the electrons each occupy their own tiny volumes. But Heisenberg's uncertainty principle says that you can't know the position and momentum of a particle with absolute certainty. So as the particles become more and more constrained in space, the uncertainty in their momentum, and hence their velocity, must go up.

So the more a star is compressed, the faster electrons will wiggle around, and that creates an outward pressure. This electron Degeneracy pressure would prevent the star from collapsing completely. Instead, it would form a white dwarf with a density much higher than a normal star. And remarkably enough, astronomers had observed stars that fit this description. One of them was Sirius B.

But the relief from this discovery was short lived. Four years later, 19 year old Subramanian Chandrasekhar traveled by boat to England to study with Fowler and Arthur Eddington, one of the most revered scientists of the time. During his voyage, Chandrasekhar realized that electron Degeneracy pressure has its limits. Electrons can wiggle faster and faster, but only up to the speed of light.

That means this effect can only support stars up to a certain mass, the Chandrasekhar limit. Beyond this, Chandrasekhar believed not even electron Degeneracy pressure could prevent a star from collapsing. But Eddington was not impressed. He publicly blasted Chandrasekhar, saying there should be a law of nature to prevent a star from behaving in this absurd way.

And indeed, scientists did discover a way that stars heavier than the Chandrasekhar limit could support themselves. When a star collapses beyond a white dwarf, electrons and protons fuse together to form neutrinos and neutrons. These neutrons are also fermions, but with nearly 2000 times the mass of an electron, their Degeneracy pressure is even stronger. So this is what holds up neutron stars.

There was this conviction among scientists that even if we didn't know the mechanism, something would prevent a star from collapsing into a single point and forming a black hole, because black holes were just too preposterous to be real. The big blow to this belief came in the late 1930s, when J. Robert Oppenheimer and George Wolkoff found that neutron stars also have a maximum mass. Shortly after, Oppenheimer and Hartland Snyder showed that for the heaviest stars, there is nothing left to save them when their fuel runs out, they wrote, this contraction will continue indefinitely.

But Einstein still couldnt believe it. Oppenheimer was saying that stars can collapse indefinitely. But when Einstein looked at the math, he found that time freezes on the horizon. So it seemed like nothing could ever enter, which suggested that either there's something we don't understand or that black holes can't exist.

But Oppenheimer offered a solution to the problem. He said to an outside observer, you could never see anything go in, but if you were traveling across the event horizon, you wouldn't notice anything unusual and you'd go right past it without even knowing it. So how is this possible?

We need a spacetime diagram of a black hole. On the left is the Singularity at r zero. The dotted line at r two m is the event horizon. Since the black hole doesn't move, these lines go straight up in time.

Now let's see how ingoing and outgoing light rays travel in this curved geometry. When youre really far away, the future light cones are at the usual 45 degrees. But as you get closer to the horizon, the light cones get narrower and narrower until right at the event horizon, theyre so narrow that they point straight up. And inside the horizon, the light cones tip to the left.

But something strange happens with ingoing light rays. They fall in, but they don't get to r equals two m. They actually asymptote to that value as time goes to infinity. But they don't end at infinity, right? Mathematically, they are connected and come back in, and they're traveling in this direction.

And this bothered a lot of people. It's bothered people like Einstein because he looked at these equations and went, well, if nothing can crosse this sort of boundary, then how could there be black holes? How could black holes even form? So what is going on here?

Well, whats important to recognize is that this diagram is a projection. Its basically a 2d map of four dimensional curved spacetime. Its just like projecting the 3d Earth onto a 2d map. When you do that, you always get distortions.

There is no perfectly accurate way to map the Earth onto a 2d surface. Different maps can be useful for different purposes. For example, if you want to keep angles and shapes the same, like if you're sailing across the ocean and you need to find your bearings, you can use the Mercator projection. That's the one Google maps uses.

A downside is that it misrepresents sizes. Africa and Greenland look about the same size, but Africa is actually around 14 times larger. The gall Peters projection keeps relative sizes accurate, but as a result, angles and shapes are distorted in a similar way. We can make different projections of 4d spacetime to study different properties of it.

Physical reality doesn't change, but the way the map describes it does. He had chosen to put a particular coordinate system over space and have a time coordinate, and off you go. It's the most sensible thing to do, right.

People realize that if you choose a different coordinate system by doing a coordinate substitution, then the Singularity at the event horizon disappears, it goes away, that problem goes away, and things can actually cross into the black hole.

What this tells us is that there is no real physical Singularity at the event horizon. It just resulted from a poor choice of coordinate system.

Another way to visualize whats going on is by describing space as flowing in towards the black hole like a waterfall. As you get closer, space starts flowing in faster and faster. Photons emitted by the spaceship have to swim against this flow, and this becomes harder and harder the closer you get. Photons emitted just outside the horizon can barely make it out, but it takes longer and longer.

At the horizon, space falls in as fast as the photons are swimming. So if the horizon had a finite width, then photons would get stuck here. Photons from everything that ever fell in. But the horizon is infinitely thin. So in reality, photons either eventually escape or fall in. Inside the horizon, space falls faster than the speed of light, and so everything falls into the Singularity.

So Oppenheimer was right. Someone outside a black hole can never see anything enter, because the last photons they can see will always be from just outside the horizon. But if you yourself go, you will fall right across the event horizon and into the Singularity.

Now, you can extend the waterfall model to cover all three spatial dimensions. And that gives you this, a real simulation of space flowing into a static black hole made by my friend Alessandro from Scienceclick. Later, we'll use this model to see what it's like falling into a rotating black hole.

Now, I've never been sucked into a black hole, but sometimes it feels like it when I'm stuck on the phone with a spam caller. Fortunately, today's sponsor, incogni, can help.

Science, Technology, Innovation, Black Holes, Einstein's Theory, Wormholes