Chapter 3: Black Holes Explained (Lecture 3)

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Alright, so today we are plunging into, well, probably the deepest, darkest concept the universe has ever thrown at us.

Uh, literally the darkest.

Exactly.

This is the ultimate cosmic drain, a region where gravity just reigns supreme and light itself is trapped forever.

We are of course talking about black holes.

And what's so fascinating to me is that the name itself, black hole, is surprisingly modern.

I mean, it was only coined in 1969.

Oh really?

By who?

By the American physicist John Wheeler.

But the idea, the profound idea of an object whose gravity is so immense that nothing can escape.

Well that has roots stretching back centuries.

Right.

It's a concept that needed a whole revolution in physics to really understand.

Yeah.

You had to get from, you know, cannonballs all the way to space -time curvature before we could truly get our heads around it.

You did.

So our mission today is to trace that incredible intellectual journey.

We're going to explore what happens when stars run out of fuel and, you know, ultimately die.

And maybe more importantly how Albert Einstein's general theory of relativity gives us the complete mathematical prediction for the existence and the startlingly simple nature of these invisible objects.

The source material for this deep dives comes from a really foundational lecture on the topic.

One that weaves together the history, the stellar physics, and the modern theory of collapse.

It's a fantastic guide.

It is.

And to really appreciate this, this final extreme fate of matter, we have to start with the original classical idea.

We're talking about the 18th century.

A time when physicists were still debating what light even was.

Exactly.

Back then, Sir Isaac Newton's ideas were completely dominant.

And the main theory was that light was made of these little discrete particles, these tiny corpuscles.

Right.

And if light is made of particles, then just basic newtonian gravity says those particles have to be affected by gravity.

Just like anything else, a cannonball, a planet, whatever.

And that very simple logical deduction led to one of the most astonishing predictions in the history of physics.

In 1783, a Cambridge Dawn named John Mitchell.

An exceptionally original thinker, from what I've read.

Oh, absolutely.

He presented a paper to the Royal Society of London.

And in it, he mathematically showed that if a star were massive enough and compact enough, its escape velocity would actually be greater than the speed of light.

He basically proposed a cosmic trap.

He argued that any light trying to leave the surface of a star like that would just get dragged back by the star's immense gravity before it could get very far.

He called them black voids in space.

What a name.

An incredible name.

But what's really insightful about Mitchell's idea is that he didn't just see them as some theoretical curiosity.

He suggested there might be a lot of these invisible stars out there.

And we couldn't see them, obviously, but we could find them.

Yes.

We could deduce they were there by the intense gravitational pull they would exert on other visible stars orbiting them.

That's basically the blueprint for how we detect black holes today.

It is a nearly perfect prediction, more than two centuries before we actually found one.

And he wasn't alone, was he?

The Marquis de Laplace, the famous French mathematician,

he came up with a similar idea independently.

He did.

And the story with Laplace is always so interesting.

He actually included the idea in the first and second editions of his big work, The System of the World.

But then he took it out.

He did.

He removed it from all the later editions.

Why do you think he did that?

Was it just too weird for the time?

Or did he spot the flaw in the argument?

I think it was probably a bit of both.

The idea was certainly out there, but there was also a really fundamental scientific problem with the Newtonian approach.

Which was what?

Well, Michel and Laplace were treating light particles like cannonballs.

You fire a cannonball up, gravity slows it down, it stops, and it falls back.

Right.

But we know now, thanks to Einstein, that the speed of light is constant.

It doesn't slow down.

A photon leaving a star has to maintain that speed, no matter how strong the gravity is.

So Newtonian mechanics couldn't explain how gravity could affect light without changing its speed.

Exactly.

It couldn't be about slowing it down.

It had to be about bending its path.

So you needed a whole new theory of gravity.

You did.

And that theory finally arrived in 1915 with Einstein's General Relativity.

It completely redefined gravity, not as a force, but as the curvature of space -time itself.

But even with the right math, it took, well, it took decades for scientists to really accept the full, terrifying implications of what happens when a star collapses.

So to really get a handle on the extreme end of a star's life, we first need to understand the incredible balancing act that keeps it going for billions of years.

Right.

Let's talk about the life cycle.

Every star begins its life through gravity.

You start with these huge clouds of gas, mostly hydrogen.

And they just start to collapse in on themselves because of their own gravity.

Exactly.

And that collapses the engine.

As the gas falls inward, the atoms bump into each other faster and faster, and the core just heats up to incredible temperatures.

And eventually it gets so hot, so dense, that the hydrogen atoms, which normally repel each other, are forced to fuse together to form helium.

Nuclear fusion.

The source describes it as being like a controlled, continuous hydrogen bomb explosion at the star's core.

Pretty good description.

It is, because that fusion process releases a staggering amount of heat and energy, and all that energy creates this immense outward pressure.

And that's the counter force.

You've got gravity pulling in, and you've got this fusion pressure pushing out.

And when those two forces are perfectly balanced, the star stops contracting.

It settles down into a long, stable period of its life.

I've always liked the balloon analogy for this.

It's a good one.

The air pressure inside the balloon is like the heat from fusion pushing out.

And the tension in the rubber is like gravity pulling in.

As long as they match, the balloon or the star is stable.

But that stability is always temporary, because the star is constantly burning its fuel.

Eventually the hydrogen in the core starts to run out, the fusion slows down, and that outward pressure starts to drop.

And this is where that great paradox of stellar lifetimes comes in, which can be a bit counterintuitive.

You'd think a bigger star with more fuel would live longer.

But it's the complete opposite.

The most massive stars burn out the fastest.

So why is that?

Why does having more gravity mean a shorter life?

Because the more massive the star is, the stronger its own gravity is.

And to fight that stronger gravity, it has to be much, much hotter inside.

So it needs more outward pressure to stay stable.

A lot more.

And the rate of nuclear fusion depends exponentially on the temperature.

So a massive star is just running at an incredibly high temperature, burning through its hydrogen fuel at a furious rate.

Sometimes millions of times faster than a smaller star like our sun.

The numbers really put it in perspective.

Our sun has enough fuel to last for about 10 billion years.

It's about halfway through its life now.

But a really massive star, say 30 or 40 times the mass of the sun, it might burn through all its fuel in as little as 100 million years, maybe even less, just a blink of an eye, cosmically speaking.

So once that fuel in the core is gone, the internal furnace starts to cool.

The pressure plummets.

And gravity starts winning instantly.

The star begins to contract again.

And that brings us to the fundamental question.

If fusion is gone, is there anything else?

Is there any other mechanism that can stop the final total collapse?

And that question takes us straight to one of the most remarkable breakthroughs in 20th century physics.

And one that came with a pretty intense personal and intellectual battle.

We are talking about the work of a young student named Subramanian Chandrasekhar.

Usually just called Chandra.

Right, Chandra.

He was a graduate student from India.

And in 1928, he set sail for England to study at Cambridge with the most famous astrophysicist of the day, Sir Arthur Eddington.

And it was on that voyage that he did the calculations.

He figured out the absolute maximum size a star could be and still be able to support itself against gravity after it ran out of fuel.

He did.

But before we get into the details of his finding, we have to mention that classic Eddington story.

Oh, the one about general relativity.

Yes.

A journalist apparently asked him if it was true that only three people in the world understood general relativity.

And Eddington is said to have paused for a moment and then replied, I'm trying to think who the third person is.

It just perfectly captures how dense and frankly, how distrusted the theory was at the time, even among top scientists.

It does.

And it was into this environment that Chandra introduced a new force to fight gravity, one that doesn't rely on heat at all.

It's called the Pauli Exclusion Principle.

OK, this is a really crucial concept for understanding what happens next.

The exclusion principle comes from quantum mechanics and it applies to matter particles.

What physicists call fermions, things like electrons, protons and neutrons.

Right.

So what does the principle say about how these particles have to behave when you cram them all together under intense pressure?

It states that two identical fermions cannot occupy the exact same quantum state at the same time.

And a quantum state is defined by a few things.

But for our purposes, it's the particles precise position and its precise velocity.

So when gravity is crushing the star,

forcing all these electrons, into a smaller and smaller space, they're being pushed into positions that are very, very close to one another.

So to avoid being in the same state, they have to have different velocity.

Exactly.

They have to start moving away from each other at different speeds.

And that motion, that kinetic energy creates a powerful repulsive pressure that pushes back against gravity.

It's often called degeneracy pressure.

So this quantum repulsion becomes the new support structure for the dead star.

It does.

It works beautifully.

But and this is the key.

Chandrasekhar found the critical flaw in the mechanism.

And that flaw is the speed of light.

Oh, relativity comes back into it.

It always does.

Relativity says there is a hard limit on how fast things can move.

And that means there's a maximum difference in velocity these particles can have.

They can't just move away from each other at infinite speed.

So there's a maximum possible repulsion that the exclusion principle can generate.

Precisely.

And if the star is dense enough, if gravity is strong enough, the inward pull will simply overwhelm that maximum repulsion.

And that gave him a number,

a precise limit.

It did.

Chandrasekhar calculated that if a cold dead star has a mass greater than about one and a half times the mass of our sun, a value we now call the Chandrasekhar limit, it cannot support itself.

The exclusion principle just isn't strong enough.

Gravity will always win.

And that single insight basically created the entire field of stellar remnants.

It defined the possible end states for stars.

That's right.

For any star below that limit, the exclusion principle works and it halts the collapse.

Leading to things like the white dwarf.

This is what happens to lower mass stars.

The collapse is stopped by the repulsion between the electrons.

Right.

You end up with an object about the size of the earth, a few thousand miles across, but with incredible density.

A cubic inch might weigh hundreds of tons, and they're very common.

The star orbiting Sirius is a famous white dwarf.

And if the star is a little more massive, but still under the limit, then the collapse goes even further.

It crushes the electrons into the atomic nuclei, where they combine with protons to form neutrons.

You're left with the neutron star, which is even smaller and denser.

Oh, unbelievably so.

Maybe just 10 miles in radius.

And the density is hundreds of millions of tons per cubic inch.

This was a purely theoretical prediction for a long time before we ever observed pulsars.

But the really disruptive, critical part of Chandra's work was the unavoidable conclusion for stars above that 1 .5 solar mass limit.

Yes.

If a star is too massive and it can't blow off enough of its weight in a supernova explosion or some other way.

And there's no reason for it to know it needs to lose weight.

Exactly.

Then the collapse is.

It's absolute.

The inescapable conclusion was that these stars must collapse past the point where quantum mechanics can save them.

They must shrink to a point of infinite density.

And this idea was met with, well, pretty much shock and outright hostility, especially from Chandra Sekhar's own mentor.

From Eddington, yes, he was brilliant.

He was a huge proponent of general relativity, but he simply could not accept this.

Why not?

Was it just a philosophical thing?

Yeah.

The idea of a star shrinking to zero size just seemed wrong.

It seems to be.

Eddington just refused to believe that nature would allow for something like that.

He insisted there had to be some other law of physics we hadn't discovered yet that would step in and stop the collapse.

And it wasn't just him.

Even Einstein thought that stars would never shrink to zero size.

That's right.

And this sustained skepticism, especially from someone with Eddington's authority.

It well, it caused Chandra Sekhar to just abandon this line of work for a while.

It's an incredible story.

A reminder that even the greatest scientists can struggle to accept the most extreme implications of their own theories.

Indeed.

He didn't get the Nobel Prize for this work until 1983.

So the theoretical groundwork for inevitable collapse was there.

But the full general relativistic picture of what happens next.

That had to wait until 1939 and the work of Robert Oppenheimer.

So Oppenheimer, right before his work was completely consumed by the Second World War, he was the one who applied general relativity directly to the problem of a collapsing star.

He did.

His work was absolutely pivotal.

But as you say, it was sort of tragically lost in the shuffle of history and really only rediscovered and appreciated in the 1960s when observation started to catch up.

He provided that crucial mathematical bridge showing what Einstein's equations really predict for a massive body collapsing under its own weight.

And that brings us to how general relativity actually defines the boundary of a black hole, the event horizon.

So when we talk about general relativity, we're not talking about a force pulling things.

We're talking about the fabric of space time itself being warped or curved.

That's the fundamental idea.

And that warping of space time dictates how everything moves, including light.

We can visualize this using something called light cones.

OK, describe a light cone for us.

Imagine you're standing still and you set off a flash of light in all directions.

The path that light traces out as it moves into the future forms a cone shape in four dimensional space time.

Gravity essentially tilts those cones.

The stronger the gravity.

The more the cones are tilted inward toward the object creating the gravity.

And we know this actually happens.

The famous solar eclipse experiments that Eddington himself led.

They showed starlight bending as it passed by the sun, just as the theory predicted.

Exactly.

So now let's just scale that effect way, way up.

As a massive star collapses, the gravitational field at its surface gets unbelievably strong.

So the light cones at the surface get tilted more and more inward.

More and more.

It gets harder and harder for light to actually escape the star's pull.

From far away, you'd see the light from the star get dimmer and also get stretched out, appearing redder.

And this process continues until the star shrinks down to a very specific size, the critical radius.

What happens at that exact point?

At the critical radius, the gravitational field is so powerful that the light cones are bent inward so severely that light trying to travel outward just can't.

It either travels parallel to the surface, trapped in orbit, or it just falls back in.

And because nothing can travel faster than light.

If light can't escape, nothing else can either.

That is the point of no return.

That's the region we call a black hole.

And the boundary, that surface of no return, is the event horizon.

The event horizon isn't a physical surface you'd crash into.

It's just the boundary in space time defined by those trapped light rays.

An astronaut falling through it might not even feel anything special at that exact moment.

But once you cross it, your fate is sealed.

Your fate is sealed.

The curvature of space time inside is so extreme that your future path must end at the center of the black hole.

There is no other direction to go.

OK, so if we're watching this whole collapse from a safe distance on a spaceship, what would we actually see?

This gets into the really strange territory of relativistic time.

It does.

And the first thing you have to just accept is that in general relativity, there is no single absolute time.

Time is relative, it's personal, and it's deeply affected by gravity.

We even see this effect here on Earth, right, just in a tiny way.

We do.

A clock at sea level runs just a tiny, tiny bit slower than a clock on top of a mountain because gravity is slightly stronger at sea level.

So let's run the thought experiment.

We've got an astronaut on the surface of the collapsing star, and they're sending us a radio signal every second, according to their watch.

As the star shrinks toward that critical radius, we on the orbiting ship would notice that the time between each arriving signal gets longer and longer.

So time on the star appears to be slowing down from our perspective.

Drastically.

Now, let's say the star reaches that critical radius at exactly 11 .00 a .m.

on the astronaut's watch.

The signal they send at 10 .59 and 59 seconds arrives, you know, a bit late, but it gets to us.

But the signal the astronaut sends right at 11 .00 a .m.

It never arrives.

It never arrives.

We on the ship would literally have to wait for an infinite amount of time for that 11 .00 a .m.

signal to reach us.

And that's not because the astronaut's transmitter broke.

It's because that final moment of their time gets stretched out over all of our future time.

That's exactly it.

And this has a direct effect on the light waves themselves.

We mentioned the light gets redder.

This is the gravitational redshift.

Can you explain that a bit more clearly?

Sure.

Think of light as a wave as that wave has to climb up and out of this incredibly deep gravitational well.

It loses energy.

The gravity is literally pulling energy out of the light itself.

And the energy of light is its color.

Right.

High energy light is blue with a short wavelength.

Low energy light is red with a long wavelength.

So as the light loses energy, its wavelength gets stretched out, shifting it down the spectrum towards red.

So from our spaceship, we would see the star appear to freeze right at the event horizon.

It would get redder and redder and dimmer and dimmer until it just fades out of existence, leaving behind only a black void.

But here's the really critical point.

The star disappears from view, but its gravity is still there.

The spaceship continues to orbit this black hole just as it orbited the star.

How does that work?

How does the gravity persist when the light doesn't?

This really highlights the difference between the gravitational field and the signals like light that are emitted from the star's surface.

The mass is still there.

The warping of spacetime caused by that mass is still there.

And that's what gravity is.

So the field itself isn't something that has to escape in the same way light does.

Precisely.

The gravitational field is a property of the space around the object.

So our spaceship just keeps orbiting as if nothing has changed, except that the star it's orbiting has gone completely dark.

It's profound demonstration that gravity truly is the geometry of space.

OK, so that's what the outside observer sees.

But what about the poor astronaut who falls past the event horizon?

Their journey is very, very different.

It is.

And this brings us to the most extreme prediction of general relativity,

the singularity and with it, the need for something called cosmic censorship.

Right.

This is where we get into the work that you and Roger Penrose did back in the mid 60s to the early 70s, which proved what has to happen inside the black hole.

What we showed using the mathematics of general relativity is that once a body collapses past its event horizon, gravity will inevitably crush it all the way down to a point of infinite density.

The singularity, a point with zero size and infinite density.

It's conceptually like the Big Bang, but in reverse.

That's a good way to think about it.

For the astronaut and the matter of the star, it's not the beginning of time.

It's the absolute unavoidable end of time.

And the major problem with the singularity is that at that point of infinite density, our known laws of science just break down.

They cease to apply.

They do.

Our ability to predict the future based on the present just completely evaporates at a singularity, which is a huge problem for physics, a profound problem.

But importantly, those of us on the outside are protected from this failure predictability by the event horizon.

And that idea led Roger Penrose to propose the cosmic censorship hypothesis in 1969.

I love the famous paraphrase of this.

God abhors a naked singularity.

So let's define what the weak version of that hypothesis states.

The weak censorship hypothesis basically says that any singularity formed by gravitational collapse must always be hidden from the outside universe by an event horizon.

It has to be decently clothed, so to speak.

And why is that so important?

Because if you could see a singularity, if it were naked,

then the unpredictability at its core could leak out into the rest of the universe and it would destroy our ability to make predictions about anything, anywhere.

The event horizon acts as a cosmic quarantine zone.

So the outside world is safe.

But what about the astronaut inside?

This is where the strong censorship hypothesis comes in.

What's the difference?

The weak version is about protecting us on the outside.

The strong version is about what happens on the inside.

It deals with the astronaut's future.

Now, theoretically, the equations of general relativity do allow for some very strange solutions where an astronaut might fall in and miss the singularity.

The so -called wormhole idea.

Right.

Passing through a wormhole and emerging in another part of the universe or even another universe entirely.

That sounds amazing, but you suggest these solutions are probably not physically realistic.

We believe they're highly unstable.

The tiniest disturbance, like the gravity from the astronaut themselves or even a single stray particle, would cause the space time inside to change dramatically, ensuring that the singularity is always in the astronaut's future.

You can't avoid it.

The collapse is terminal.

So the strong censorship hypothesis is really a statement that the universe preserves cause and effect.

It says singularities are always in our future, like in a black hole or in our past, like the Big Bang.

That's it.

Exactly.

If this hypothesis failed, if stable, naked singularities could exist, the implications would be chaotic.

Some models suggest you could even travel into the past near one, which raises all sorts of dangerous paradoxes.

The classic go back and stop your grandparents from meeting problems.

Exactly.

And we believe physics has built in protections to prevent that kind of causal breakdown.

And that protection is the event horizon.

OK, so moving from that unpredictable interior to the very predictable exterior,

we get to one of the most elegant and frankly simplifying results in all of physics, the no hair theorem.

Yes.

When a star actually collapses, it's a very messy, violent event.

The star could be lumpy, it could be pulsating, it could be shaped like a potato for all we know.

And for a long time, the assumption was that the final black hole would carry some memory of that initial messiness.

That was the logical assumption.

But the key is what happens during the collapse itself.

The process creates these violent ripples in space time gravitational waves.

And those waves carry away energy.

They do.

And in doing so, they carry away all the irregularities of the collapsing star.

The analogy I like is a collapsing ball of fluid.

No matter how messy the initial splashes, it will eventually settle down into a perfectly smooth, calm sphere.

The black hole does the same thing, just with gravitational radiation instead of viscosity.

Exactly.

And the first huge theoretical step here came in 1967 from a physicist named Werner Israel.

What did he prove?

He proved that any non -rotating black hole must settle down into a state that is perfectly spherical, and its size would depend only on its mass.

That's it.

A profound simplification.

It meant the final state was just the simplest possible solution to Einstein's equations.

The Sturtschild solution from 1917.

It was.

But initially, people were a bit worried by the result.

Why?

Well, Israel and others thought since real stars are never perfectly spherical,

maybe his proof meant that only a perfectly spherical star could form a proper black hole and that the collapse of any real lumpy star must lead to a naked singularity.

Oh, I see.

But the other interpretation, the one championed by Penrose and Wheeler, was the fluid analogy that no matter how lumpy the star was to begin with, the gravitational waves would smooth it out into that perfect sphere.

And that's the view that won out.

But of course, most stars rotate.

Our sun rotates, which makes it bulge a bit at the equator.

So the simple non -rotating solution wasn't the full picture.

And that's where the work of Roy Kerr, a New Zealander, comes in.

In 1963, he found a more general solution for rotating black hole.

The Kerr black hole.

Right.

And they aren't perfect spheres.

They bulge at the equator, just like a spinning planet.

But critically, their final size and shape depend on only two things, their mass and their rate of rotation.

So the immediate guess was that any real rotating star that collapses would eventually settle down into one of these Kerr solutions.

That was the conjecture that all the other messy details of the original star, its chemical makeup, its magnetic fields, its mountains and valleys would all be radiated away.

And proving that was a huge undertaking.

It was.

It happened in stages.

First, Brandon Carter showed that if a rotating black hole was stable and had an axis of symmetry, its properties were limited to just mass and rotation.

And then the next year, in 1971, you proved the next crucial piece.

I showed that any stationary rotating black hole must have that axis of symmetry.

Which then allowed David Robinson in 1973 to put all the pieces together and prove the final conjecture.

The end state had to be the Kerr solution.

It did.

And all of this work is summed up in that amazing maxim.

A black hole has no hair.

Why that phrase?

And what does the loss of that hair really mean?

The hair is just a metaphor for all the complex individual characteristics of the original star.

To describe a person, you need to know their height, their hair color, their eye color, and so on.

A black hole, in contrast, is bald.

It can be described completely by just two numbers, mass and rotation.

All that information, all that history is just erased.

It's lost to the outside universe.

And that simplification is what makes black holes so powerful to study.

It means that to model any black hole, whether it formed from a star made of iron or a star made of hydrogen, we only need those two final numbers.

It makes the theory beautifully clean and testable.

Which brings us to the big question, do they actually exist?

For a long, long time, black holes were just seen as this weird mathematical outcome of a theory that a lot of people still found.

Dubious.

They call general relativity the dubious theory.

Opponents question their existence precisely because the idea seemed too strange to be real.

But the first real, tangible clues that these extremes of gravity were at play in the universe started showing up in the mid -1960s with the discovery of quasars.

That's right.

In 1963, an astronomer named Martin Schmidt was studying a faint star -like object called 3C273.

It was also a very powerful radio source.

And when he measured its redshift, the number was just staggering.

And to be clear, if that redshift was caused by gravity,

the object would have to be so massive and so close to us that it would be messing with the orbits of the planets in our own solar system.

Which it obviously wasn't.

So the only other explanation was that the redshift was cosmological.

It was caused by the expansion of the universe.

Which meant the object was incredibly far away.

Billions of light years.

Exactly.

And for something to be visible from that distance, it had to be pumping out an unbelievable amount of energy equal to hundreds of entire galaxies, all from a region no bigger than our solar system.

That level of energy was just impossible to explain with any known process, like stars burning.

The only mechanism that could possibly generate that much power was gravitational collapse on a massive scale.

Not just one star, but maybe the entire central region of a galaxy falling into a supermassive black hole.

So quasars weren't direct proof, but they were powerful evidence that massive gravitational collapse was really happening out there.

They were.

And then more support came in 1967 when Jocelyn Bell, a research student at Cambridge, discovered pulsars.

These were objects that were emitting these incredibly regular, sharp pulses of radio waves.

So regular, in fact, that the team initially joked they might have found signals from aliens.

They labeled the first few, LGM 1, 2, 3, 4 little green men.

But the reality was almost as profound for physics.

They were rapidly rotating neutron stars.

Yeah.

And the discovery of neutron stars was the critical missing link in the argument for black holes.

Why was that?

Because it proved that matter could collapse to these extreme densities, down to a radius of just 10 miles or so.

And that's only a few times bigger than the critical radius for a black hole.

So if nature allowed stars to collapse that far, it's not a huge leap to think that more massive stars would be pushed over the edge and collapse all the way.

It made the whole idea seem much more physically plausible.

So with the theory looking more solid, how do you actually find one?

We come back to Mitchell's idea from 1783.

You look for its gravity.

You look for binary star systems, a visible star orbiting an unseen companion.

The trick is to find one where the unseen companion is too massive to be a white dwarf or a neutron star.

And the classic most famous example of this is the system called Cygnus Xi.

Yes, a very strong X -ray source in the constellation Cygnus.

You have a huge visible blue supergiant star and it's orbiting something we can't see.

And those X -rays are the key, right?

They're the telltale sign.

They are.

What's happening is that gas is being blown off the surface of the visible star and it's being captured by the gravity of the unseen object.

This gas then spirals inward, forming what's called an accretion disk.

Like water going down a drain.

A perfect analogy.

And as that gas gets closer and closer, it gets accelerated and heated to millions of degrees.

And it starts emitting these intense X -rays right before it falls over the edge.

And that tells you the object has to be really small and dense.

It does.

But the final piece of evidence comes from the orbit.

By watching the motion of the visible blue star,

astronomers can calculate the minimum possible mass of its unseen partner.

And for Cygnus Xi, that minimum mass is about six times the mass of our sun.

Six solar masses, which is way over the Chandrasekhar limit of 1 .5 for a white dwarf.

And it's also over the absolute maximum mass for a neutron star, which we think is around three solar masses.

So it can't be a white dwarf.

It can't be a neutron star.

The only thing left is a black hole.

It's the only natural explanation that fits all the data.

It's a very compelling case.

And it led to my famous long running bet with Kip Thorne at Caltech.

Tell us about the bet.

Well, back in 1975, I bet him that Cygnus Xi did contain a black hole.

Kip bet that it didn't and that we'd find some other explanation.

At the time, we were maybe 80 percent sure.

Now, after decades more data, that certainty is well over 95 percent.

I've since conceded the bet, but it shows you just how big of a scientific leap it was to finally confirm these things were real.

And today we've found many more like it.

And of course, supermassive black holes at the center of our own galaxy and pretty much every other.

So all the black holes we've talked about so far form from collapsing stars, which means they have to be more massive than the Chandrasekhar limit, at least 1 .5 times the mass of the sun.

But the theory doesn't forbid smaller ones, does it?

Can you have some Chandrasekhar black holes?

You can, but they absolutely cannot form from a star collapsing.

A star that small has no problem supporting itself as a white dwarf.

So to make a small black hole, you need something else.

You need a huge amount of external pressure to squeeze the matter together.

An enormous amount of pressure, yes.

You can't rely on the object's own self -gravity.

The source material mentions John Wheeler's thought experiment about this.

The one with the hydrogen bomb.

Right.

He calculated that if you could somehow build a hydrogen bomb using all the heavy water on Earth, the compression at the center of that explosion might be enough to create a tiny black hole.

But as he pointed out, no one would be around to see it.

Exactly.

So the only practical natural place to find those kinds of pressures is in the very, very early universe.

This brings us to the idea of primordial black holes.

The conditions in the first fractions of a second after the Big Bang, the temperatures, the pressures were staggering.

And if the early universe wasn't perfectly smooth and uniform, which we know it wasn't.

We know it wasn't.

If there were tiny regions that were just a little bit denser than average, the immense pressure of the surrounding universe could have crushed those regions into black holes.

Black holes that could be far, far smaller than any star.

Potentially, yes.

And the fact that we have galaxies and stars today is the ultimate proof that those early irregularities existed.

If the universe had been perfectly smooth, matter would still be spread out evenly everywhere.

So finding primordial black holes would tell us a huge amount about what the universe was like in its very first moments.

It would be a direct window into the initial conditions of the Big Bang itself.

But detecting them is incredibly difficult.

A large one, say bigger than a billion tons, would still be microscopic.

And we could only hope to detect it by its subtle gravitational pull on things around it.

And that leads us to the final, really paradoxical idea that completely changed how we think about black holes linking gravity to quantum mechanics.

It does.

For centuries, the defining feature of a black hole was that it's black.

Nothing gets out.

But we now understand that this isn't strictly true.

Black holes are not completely black.

They glow.

And the craziest part is, the smaller the black hole is, the more intensely it glows.

Which means those tiny primordial black holes might actually be the easiest ones to detect, not through their gravity, but through their own radiation.

The ultimate irony, the blackest objects in the universe might actually be shining.

It's the perfect cliffhanger to a long and incredible theoretical journey.

What an incredible trip.

We've gone from 18th century Newtonian physics all the way to the quantum edge of cosmology.

Let's just try to recap the key takeaways from this deep dive.

Well, we saw that the basic idea of a cosmic trap is very old, going back to Michelin and Laplace.

But to really understand black holes, you need Einstein's general relativity.

And the fate of a star is sealed by the Chandrasekhar limit.

If it's over about 1 .5 times the mass of the sun,

collapse is absolutely inevitable.

And once that event horizon forms, the black hole itself becomes incredibly simple.

The no hair theorem tells us all that complex history is erased, leaving only mass and rotation.

And even though the idea faced so much resistance,

the observational evidence from the huge energy output of quasars to the precise orbital mechanics of systems like Cygnus XI has really confirmed that these things are out there and they're a fundamental part of our cosmos.

They absolutely are.

And this whole journey leaves us right at the frontier, doesn't it?

Connecting these huge gravitational objects to the moment of creation.

It does.

That question of whether primordial black holes exist is directly tied to the fundamental question of how uniform or how lumpy our universe was in its first moments.

And understanding that paradoxical glow we talked about, radiation from black holes, is the next huge step.

It's where the immense scale of gravity finally meets the subatomic world of quantum mechanics.

And that's a connection that continues to challenge everything we think we know.

A perfect thought provoking place to end our deep dive into the world of black holes.

Thank you so much for joining us.