What is a black hole? Part 3: Plunging in

What is a black hole? Part 3: Plunging in

Have you ever wondered what it would be like to fall into a black hole? To see what happens inside the darkness?

In this post we will plunge right in. We will experience what will happen to our bodies as we fall into a black hole. We will see that there is light as well as darkness inside it. And we will also learn how the unavoidable death that awaits us far inside the black hole is, luckily, of a rather merciful type.

 

A black hole reminder

Before we start our journey, let us remind ourselves of what a black hole actually is. Or rather: what a black hole isn’t.

A black hole isn’t like a planet or a star. Stars and planets are material objects that occupy a region in space and change with time. Black holes, on the other hand, are made out of space and time themselves. They are what relativity theorists call spacetime geometries.

That space and time can change means that the angular sum of triangles doesn’t have to be 180 degrees and that clocks can tick at different rates at different points. This will, in turn, affect the trajectories of light and matter. A black hole is therefore less of an object and more of a bizarre twist in space and time that determine how light and matter must move.

We will journey into the least complex example of a black hole: one that is not rotating and does not have any electric charge. The mathematical formula for such a black hole was discovered by the German astronomer Karl Schwarzschild in 1915. They are therefore sometimes called Schwarzschild black holes. Although black holes that are rotating have a more complex structure, the Schwarzschild formula contains the most important property of black holes: the existence of an event horizon.

The event horizon is the black hole’s surface. This surface is not made out of solid matter, like the surface of the Earth, or a tenuous gas, like the surface of the Sun. Instead, the black hole’s surface is made entirely out of space and time. It’s therefore perfectly possible to pass through it, just in the same way that you are moving through space and time right now.

But there is a caveat. You can only pass the event horizon in one direction: from the outside to the inside. Inside the black hole space and time curve in such an intense way that no direction leads out of the black hole. Nothing, not even light, can escape from the black hole’s interior. A black hole is therefore the ultimate cosmic prison. 

The event horizon is not only a surface of no return, but also a boundary of our knowledge. Because of the one-way nature of the event horizon, it’s impossible to determine from the outside what is happening on the inside. The only way to learn what is going on inside a black hole is therefore to plunge right in.

 

Safety first

But what are the perils of our plunge?

In a sense, black holes are less dangerous than the Earth or the Sun. When we fall towards the Earth, we hurt ourselves when we hit the ground. When we fall towards the Sun, we burn up. But when we fall towards a black hole, we can travel through its surface and continue our journey on the inside.

There exists, however, a lethal problem: we might get ripped apart before we reach the event horizon. The real danger when we fall towards a black hole are what’s known as tidal forces. If we fall feet first towards the black hole our feet will accelerate faster than our head. Our body will be stretched out along the direction of our fall and compressed at the sides. This effect is called tidal forces, because a similar effect from the gravitational field of the Moon gives rise to the oceanic tides on the Earth. In the context of black holes, the effect is also called “spaghettification”. Our main concern is thus to avoid getting stretched out like a piece of pasta!

Luckily, the tidal forces are weaker for larger black holes than smaller ones. This might feel counterintuitive. Shouldn’t a large black hole be more dangerous than a small one? The answer is no. Tidal forces depend on how much the gravitational field around the black hole changes over the distance of your body. For a small black hole, say one that is only a few tens of kilometers across, the gravitational field will change dramatically over the distance of your body as you approach the black hole. You will therefore be ripped apart before you even have a chance to reach the event horizon.

But for a large black hole, say one that is several millions of kilometers across, the gravitational field will stay roughly the same over the length of your body as you approach the event horizon. You can safely travel into the black hole without the danger of tidal forces ripping you apart. Size matters, or rather, relative size matters: it’s your size versus the size of the black hole.

In fact, size is the only thing that characterises a Schwarzschild black hole. To describe it, all you need is a single number. It turns out that this number, called the Schwarzschild radius, is directly related to the mass of the black hole. Larger radius equals larger mass, and larger mass equals a safer journey to the inside.

That being said, let us choose a big and massive black hole and dive straight in.

 

Distorted stars

We’re floating in space.

In front of us lies our destination: a black hole that is as massive as 10 billion suns. It is 60 billion kilometers across, which is several times larger than our solar system.

We’re far away from the black hole. It just looks like a dark circular patch in the sky.

 

The smallest known wandering black hole

Around it you see the light from distant stars. Their appearance look distorted. It’s as if the star light passes near the black hole in weird circular arcs. When you look closely through the magnifying function in your space helmet you can even see the star light from the stars behind you.

“The black hole curves space and time so strongly that light can travel on bent trajectories around it,” you hear me say over the radio. “Light that comes from behind us can reach the vicinity of the black hole without going into it. The light will fly around it and then come back towards us.”

“Sorry, but who are you?” you reply.

“I’m your spacetime chaperone,” you hear me answer. “My job is to guide you safely into the black hole.”

You turn to your right and look at me. You see a white spacesuit and a gold covered visor on the space helmet. You can’t discern any face.

“Have you done this before?” you ask.

“Uhm, no. You can only go into a black hole once. This is my first time.”

“Doesn’t sound very trustworthy to me.”

“I’ve studied the math. It will guide us into the black hole.”

“And you trust the math?” you ask.

“Look!”, you hear me say. You see me pointing towards the black hole. It has grown in size. “We’re approaching the event horizon.”

 

Towards the surface of no return

The black patch in the sky has grown. Although the darkness has become bigger, you don’t feel anything special. We’re just floating in space in much the same way that astronauts onboard a space station float in space. If it wasn’t for the distant stars that we use for navigation, we wouldn’t even know when we’re passing the event horizon. In a void universe a black hole would just be darkness surrounded by darkness, emptiness in emptiness. Thanks to the distorted starlight and Schwarzschild’s formula, we have a chance of knowing when we pass the surface of no return.

“I’ve read that time slows down near a black hole compared to clocks far away,” you say. “But I don’t feel that time is getting slower. The clock projected on my visor ticks as usual. One second is one second, and we’re talking to each other in a perfectly normal way.”

“That’s right,” you hear me reply. “One second for us will always be one second. It’s when we compare that second to clocks far away from us that there will be a difference. Our second can represent several hours or even thousands of years for someone who stays at a large distance from the black hole. It all depends on how close we are to the event horizon.”

“So while we had this conversation entire lifetimes could have passed on our Earth?”

“Yes.”

“And since we haven’t passed the event horizon we could in principle turn around and go back home?”

“Yes, if our rockets are strong enough.”

“So if we manage to turn around close to the event horizon and then go back home, we could discover that our parents and children have passed away, that new generations have taken their place, that our society and planet could have changed over a time span of thousands of years? Even though we only spent a short time near the black hole?”

“Yes.”

“That sounds like science fiction,” you say. “How extreme can this effect be?”

“If you compare how slow clocks run at the surface of the black hole compared to clocks far away, the time difference is infinite. For someone far away from the black hole, time seems to be standing still on its surface. At least in theory: in practice it’s impossible to stay put at the event horizon with a clock and send signals to a far away observer. But if you managed to stay a few hours right above the event horizon it could in principle correspond to millions or even billions of years further away.”

 

Time to death

As you look at the stars, which themselves lie thousands of light years away from the black hole, you can’t help but wonder if there is life on the planets orbiting those stars. Could there be entire civilisations there? Have millions of years passed on their planets while you were approaching the event horizon? Does it even make sense to think of what happens on other planets ‘now’ if the relativity of time becomes so extreme near the black hole?

“I did a little calculation,” you hear me say over the radio.

“A little calculation?” you ask.

“Yes. Inside the black hole is a singularity. It’s a point where the spacetime curvature becomes infinite. The tidal forces near the singularity will rip us apart. I want to know how long time it will take from the moment that we pass the event horizon until we reach the singularity.”

“Hold on!” you say. “What do you mean ‘rip us apart’? We’re going to be broken up into pieces?”

“Yes, all the way down to the subatomic level. As we approach the singularity, everything in our bodies – muscles, nerves, skeleton, cells, DNA, molecules, atoms – will be stretched out and broken up. Everything we consists of will be torn apart. It’s a gravitational death that’s impossible to experience on Earth.”

You turn towards me and stare at my visor. “I’m not sure this is what I wanted. Can’t we just avoid the singularity? We have some pretty powerful rockets after all.”

“It’s impossible,” you hear me say. “The singularity inside a Schwarzschild black hole is not a point in space, but an instant in time. More precisely, it’s an instant in the future. Since you can’t escape the future, you can’t escape the singularity.”

“But I thought your job was to guide me safely in the black hole!”

“Safely into the black hole. Once we’re on the inside I’m afraid there’s no turning back. Our journey ends right before the singularity.”

You stay silent for a while. Maybe you could turn back before it’s too late? But you decide to continue. “Better to be dissolved into nothing than to be buried in dirt,” you think before you say over the radio: “You said we will die before we reach the singularity. But what actually happens at the singularity?”

“Nobody really knows for sure. Schwarzschild’s formula indicates that the spacetime curvature blows up near the singularity. But the singularity itself isn’t even a part of space and time: it’s just a sign that our model breaks down and that we can’t predict what will happen.”

“I heard statements that space and time ends at the singularity. Is this correct?”

“Not really. It’s our knowledge that ends at the singularity, not space and time. Singularities are quite common in physical theories. For example, there’s also a singularity in Newton’s theory of gravity: the gravitational force between two masses becomes infinite when their relative distance vanish. But as two masses get close to each other the electromagnetic and nuclear forces become important. So if we only use Newton’s theory we don’t get the full picture. Furthermore, Newton’s theory is just an approximation, and we must use Einstein’s theory of general relativity if we want to understand how gravity works under more extreme conditions. But Einstein’s theory is also limited. We can use it to predict what will happen inside a black hole. But at the singularity we need a new theory, some kind of quantum theory of gravity, to predict what will happen. And we don’t have that yet.”

You sigh. “It feels like you physicists don’t really have a clue what goes on at the final moment inside a black hole.”

“That’s a perfectly accurate statement,” you hear me reply. “But as the relativist Charles W. Misner put it, we should regard the singularity ‘not as a warning of our ignorance, but as a source from which we can derive much valuable understanding.'”

“Whatever. Since we will die before we reach the singularity it doesn’t really matter to me. How long time did you say we will have left to live once we pass the event horizon?”

“Right, back to my calculation.” You see me pull out a paper with some numbers scribbled down on it. “The time until we die is given by a simple formula. All you have to do is to multiply two numbers. The first number is 0.000007. The next number is the mass of the black hole in terms of solar masses.”

“And then what?” you ask.

“Then you get the time you have left to live in seconds.”

“In seconds? Give me an example.”

“Sure. Let’s say you’re going into a black hole which is twice as massive as the Sun. Such a black hole is roughly 12 kilometers across. In principle, you would be ripped apart by strong tidal forces even before you had a chance to enter the black hole, but assume for the sake of the argument that you could pass the event horizon. You would then reach the singularity after 0.000007 times 2 seconds. That’s 0.000014 seconds, or 14 microseconds. You wouldn’t even have time to blink before you’re dead.”

“Let’s avoid that kind of black hole then,” you reply. “What about those supermassive black holes?”

“If you would fall into the supermassive black hole at the centre of the Milky Way, which weighs 4 million solar masses, you could survive for 0.000007 times 4 million seconds. That’s 28 seconds!”

“Are you kidding me? What’s the point of going into such a black hole if we’re only going to survive for 28 seconds?”

“That’s why we are heading towards a black hole with 10 billion solar masses. According to my calculation, which is as simple as multiplying 0.000007 with 10 billion, we will survive for 70 thousand seconds. That’s 19 hours, almost a full day inside the black hole!”

“Almost one day inside the black hole?”

“Yeah! What will you do during all that time?”

“I don’t know,” you say. “How could you even do this calculation?”

“It all follows from the formula that Karl Schwarzschild discovered during World War I. Everything you want to know about non-rotating black holes without any electric charge is contained in that formula. It even predicts how long we will survive!”

 

Crossing the event horizon

The darkness in front of us has grown larger. Several stars that previously were further away from the black hole seems to have been pushed closer towards the black holes’ rim. They shine more brightly and with a more bluish hue. You find it remarkable how the black hole deflects the starlight trajectories so that you not only can multiple copies of the stars that are around the black hole, but also the light from stars that are behind the black hole and the light from stars that are behind you. In a sense the black hole allows you to see more of your surroundings, but in a heavily distorted way.

“According to the measurement of the distant starlight we have now passed the event horizon,” you hear me say.

“What?” you reply. “I didn’t notice a single thing.”

The black hole still seems to be in front of you. You turn around in the direction we came from. The starlight from the distant universe is still there. It looks a bit darker, but you can still see were we came from, although the distances between the stars seemed to be stretched out in a weird way.

“But the black hole still is in front of us!” you exclaim. “How can we be inside of it?”

“Think of it like a glass of water. When you put a pen in the water the apparent position of the pen seems to change. The trajectories of the light rays that comes front the pen will be refracted as the light passes through the water, glass and air. Thus the apparent position of the part of the pen that is in the water seems to change. A similar phenomena happens as we approach the black hole. First of all, the light rays from the distant stars travel on very different trajectories compared to if the black hole wasn’t there. Secondly, we’re traveling at such a high velocity now that we are experiencing relativistic effects. The entire sky seems to be pulled towards our direction of motion. Therefore the black hole seems to be in front of us even though we are inside of it. The starlight that we see concentrated around its rim also becomes more intense and blue because of our high velocity. At the same time it becomes more dark and redshifted behind us.”

“But why can’t we go back in the direction we came from?” you ask.

“For someone hovering above the event horizon in a rocket it would have appeared as if we’re passing by at close to the speed of light. And since you can’t travel faster than the speed of light, you can’t go back in the opposite direction which leads out of the black hole.”

“So we’re stuck?”

“Yes. We’re stuck inside the black hole now. We’ll have 19 hours to spend here before we reach the singularity. We don’t feel anything special right now, but eventually we will start to feel the pull of the tidal forces on our bodies.”

“How long time from that moment until we die?” you ask.

“Schwarzschild’s formula tells us that from the moment that you start to feel that your body is getting stretched out, you have about 0.3 seconds before you reach the singularity and die.”

“0.3 seconds? You mean for this particular black hole?”

“No, for all black holes. It turns out that it doesn’t matter how small or large the black hole is. It’ll always be the same: from the time you start to feel a strong thug on your body, you have about 0.3 seconds left to live.”

“That’s a very short time,” you say. “Does this always happen inside the horizon?”

“Not necessarily. For a small black hole you will feel strong tidal forces even before you reach the event horizon. From that point on, it’ll take about 0.3 seconds before you reach the singularity. “

“And you would pass the event horizon during those 0.3 seconds?”

“That’s right. For a small black hole you will feel the tidal forces outside of the event horizon, and then quickly get sucked in and get smashed near the singularity.”

“And for us right now?”

“In about 19 hours the tidal forces will be strong enough to tear us apart. Once we start to feel the tidal forces …”

“… we have 0.3 seconds before we reach the singularity, yes yes I get it.”

“It will be a merciful death,” you hear me say. “You will barely have time to notice anything before you’re dead.”

 

Plenty of room

After a couple of hours of floating in the darkness you get bored.

“So how big is it in here?” you ask. “How much stuff could you fit inside a black hole?”

“I was hoping you would ask!” you hear me reply.

You see me take out some papers from a pocket in my space suit. The papers are scribbled with equations.

“Yet another calculation,” you sigh.

“It turns out that the interior of black holes are filled with surprises,” you hear me say. “They are like pocket universes that look completely static from the outside, but that are highly dynamical on the inside. The physicists Marios Christodoulou and Carlo Rovelli computed how large black holes are in 2014. Can you guess what their answer was?”

“Shouldn’t they be just as large as we measure them to be from the outside?” you say. “That is, if we know the Schwarzschild radius we know how big they are?”

“Exactly! That’s true from the outside. But on the inside they are growing bigger with time.”

“But we don’t see that from the outside,” you reply. “The area of the surface remains fixed. And from the area of a spherical surface we should be able to calculate the volume.”

“In the absence of spacetime curvature that would be true. But since space and time curve in such a weird way around and inside a black hole there doesn’t exist a simple relationship between the area of its surface and the volume inside. Its volume can grow even though its area remains the same. It doesn’t grow in the sense that it will accumulate more matter and become larger. That can happen too. But even left completely to itself the interior of a black hole will become larger and larger with time.”

“That’s so weird”, you say.

“A black hole looks static and fixed from the outside, but is dynamical and changing on the inside. Some people like to explain this by statements such as ‘space and time switch roles on the surface of the black hole’. But that’s not something you and I experienced as we passed the event horizon. Space was space and time was time.”

“So why do people makes those statements?”

“In the formula that Schwarzschild found it does look like the coordinates we use for time and space flip roles on the inside compared to the outside. But we have to be careful with statements about coordinates. By themselves coordinates don’t have any physical meaning.”

“Let’s not get into philosophical hairsplitting now,” you sigh. “Just tell me how big a black hole is on the inside.”

“Christodoulou and Rovelli took the supermassive black hole at the centre of the Milky Way as an example,” you hear me reply. “From the outside, Sagittarius A* is roughly as large as the volume spanned by the orbit of Mercury. But after they did their calculation, Christodoulou and Rovelli exclaimed that the interior of Sagittarius A* is big enough ‘to fit a million Solar Systems!'”

“Are you kidding me?” you shout over the radio. “It appears smaller than the solar system from the outside but you could fit a million solar systems on the inside? Stop making these jokes, please.”

“That’s what the mathematics says. Our intuition about how space and time work is limited to our experience on Earth. When spacetime curvature becomes extreme our intuition doesn’t catch up. We have to trust the mathematics.”

“So how large is the 10 billion solar mass black hole we’re floating around in?”

“It depends on how long it has been around. But since it is about 2500 times more massive than Sagittarius A*, I guess that at some moment you could fit more than a billion solar systems inside of it. It’s hard to believe, but as Christodoulou and Rovelli said: ‘There is a lot of available real estate inside a black hole’.”

 

The ring of light at the end of darkness

We have been falling for more than 18 hours inside the black hole. You look around. Above your head is darkness, and below you is darkness. But in a narrow band around you a ring of light shines bright. It looks like a star-spangled hula-hoop extending far into the distance. It’s much brighter than the night sky on Earth.

“All the light from the stars and galaxies outside the black hole has been focused in the ring,” you hear me say. “Because of the intense warping of space and time the light appears in a narrow band perpendicular to our direction of motion. This is the last thing we will see before we die.”

You start to breath more heavily when you realise that your final moment is near.

“We only have a few minutes left”, you hear me say over the radio. “I enjoyed travelling with you. Unfortunately we can’t do it again.”

Your heart rate goes up. In a state of panic you move your arms and legs, as if your movement could make you escape the impending singularity.

The intense but futile movements makes you sweat. The smell of sweat spreads inside your spacesuit and triggers a childhood memory.

You were walking in the woods with one of your childhood friends on a warm summer day.

As you entered a glade, you saw an old oak. You climbed the oak and put your hands around a thick branch. You took your feet away from the oak and started hanging freely from the branch. You remember the feeling of wood against your hands and the smell of sweat in your nose.

All of a sudden you felt a thug in your feet. Your childhood friend had jumped up and grabbed your legs. The weight of your friend pulled your legs down. At the same time your muscles started to ache as you struggled to keep your grip around the branch. It felt like if you were being pulled in two directions at once.

You were afraid that if you let go of the branch you would fall and hurt yourself. But you were also afraid that if you hung on to the branch you would be ripped apart from the weight of your friend that pulled your legs down. You knew it couldn’t happen, but your child mind kept imagining the impossible.

As you see the dark abyss under and over you, the same feeling of fear arises within you. You’re afraid of falling and you’re afraid of being thorn apart. You close your eyes, take a deep breath and focus on the sensations from that summer day: the birds singing, the warm sunlight hitting your skin, the blue sky above you. But you can’t escape the feeling of your childhood friend hanging in your feet, and your heart starts to beat even more intensely as you realise that the darkness inside the black hole is starting to pull your feet down and your head up.

You open your eyes. The bright ring of light squeezed in between the darkness above and below glares at you with the force of a million stars.

Before you have time to scream, your 0.3 seconds are over.

Darkness has ripped you apart.

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