Black holes don't emit light, so the only way to see Gargantua is through its effect on light from other objects. AT Interstellar other objects are the accretion disk (Chapter 9) and the galaxy in which it resides, including nebulae and an abundant star field. For the sake of simplicity, let's include only the stars for now.

Gargantua casts a black shadow on the star field, and also refracts the rays of light from each star, distorting the star pattern visible to the camera. This distortion is the gravitational lens described in Chapter 3.

Figure 8.1 shows a rapidly spinning black hole (let's call it Gargantua) in front of a star field as it would appear to you if you were in Gargantua's equatorial plane. The Shadow of Gargantua is a completely black area. Just beyond the edge of the shadow is a very thin ring of starlight, the so-called "ring of fire", which I manually enhanced to make the edge of the shadow more defined. Outside the ring, we see a thick spray of stars in a concentric pattern created by a gravitational lens.

Rice. 8.1. A stellar pattern created by a gravitational lens around a rapidly spinning black hole like Gargantua. Seen from afar, the angular diameter of the shadow in radians is 9 Gargantua radii divided by the distance from the observer to Gargantua. [Modeled for this book by the visual effects team at Double Negative.]

As the camera moves along Gargantua's orbit, the stars appear to be moving. This movement, combined with the lens, creates spectacularly changing light patterns. In some areas, the stars stream with high speed, in others they flow calmly, in others they freeze in place; see the video on this book's page at Interstellar.withgoogle.com.

In this chapter, I explain all these nuances, starting with the shadow and its ring of fire. Later I will describe how the images of the black hole were actually obtained in Interstellar.

In portraying Gargantua in this chapter, I consider it to be a rapidly spinning black hole, which is what it should be in order to provide an extreme loss of crew time. Endurance in relation to the Earth (Chapter 6). However, in the case of fast rotation, the flattened left edge of Gargantua's shadow (Figure 8.1) and some specific features of the stellar jet and accretion disk could be confused by a mass audience, so Christopher Nolan and Paul Franklin chose a slower rotation speed - 60 percent of the maximum - for images of Gargantua in the film. See the last section in Chapter 9.

Warning: The explanations in the next three sections may require a lot of mental effort; they can be skipped without losing the thread of the rest of the book. Don't worry!

The Shadow and Her Ring of Fire

Let's say you are at the yellow dot. white rays A and B, as well as other rays like them, bring you the image of a fiery ring, and black rays A and B bear the image of the edge of the shadow. For example, a white beam A emanating from some star far from Gargantua, it moves inwards and is trapped along the inner edge of the shell of fire in the equatorial plane of Gargantua, where it flies around again and again, driven by a vortex of space, and then escapes and reaches your eyes. Black beam, also signed A, comes from Gargantua's event horizon, it moves outward and gets trapped on the same inner edge of the fire shell, then escapes and reaches your eyes side by side with the white beam A. The white beam carries the image of a piece of a thin ring, and the black one - the image of a piece of the edge of the shadow. The fiery shell is responsible for bringing them side to side and directing them into your eyes.

Rice. 8.2. Gargantua ( sphere in the center), its equatorial plane ( blue), fireshell ( pink and purple) and black and white rays, carrying the image of the edge of the shadow and a thin ring around it.

Similarly for white and black rays B, only they fall into a trap on the outer edge of the shell of fire and move clockwise (making their way towards the spatial vortex), while the rays A get trapped on the inner boundary and move counterclockwise (and the dimensional whirlwind picks them up). In figure 8.1, the left edge of the shadow is flattened, and the right edge is rounded due to the fact that the rays A(from the left edge) come from the inner border of the shell of fire, very close to the horizon, and the rays B(from the left edge) - from the outside, located much further from the horizon.

black rays C and D in figure 8.2 originate at the horizon, move outward and are trapped in non-equatorial orbits in a shell of fire, then escape their trap orbits and reach your eyes, carrying images of bits of the edge of the shadow that lie outside the equatorial plane. Beam Trap Orbit D shown in the top right inset. white rays FROM and D(not shown) coming from distant stars are trapped side by side with black beams C and D and move towards your eyes side by side with C and D, carrying images of fire ring pieces side by side with shadow edge pieces.

The lens of a non-rotating black hole

To understand the pattern of stars refracted by a gravitational lens and their jet as the camera moves, let's start with a non-rotating black hole and with rays of light emanating from a single star (Figure 8.3). Two beams of light go from the star to the camera. Each one travels in the straightest path it can in the curved space of the hole, but the curvature causes each beam to bend.

One curved beam moves towards the camera around the left edge of the shadow, the other around its right edge. Each beam carries its own image of the star to the camera. These two images as seen by the camera are shown in the inset in Figure 8.3. I circled them with red circles to distinguish them from all the other stars seen by the camera. Note that the right image is much closer to the hole's shadow than the left image. This is because its curved beam traveled closer to the hole's event horizon.

Rice. 8.3. Above: The curved space of a non-rotating black hole as seen from the bulk, and two beams of light moving through the curved space from the star to the camera. Bottom: A stellar pattern refracted by a gravitational lens as seen by a camera. [Modeled by Alain Riazuelo; see the video of his model at www2.iap.fr/users/riazuelo/interstellar.]

Every other star appears twice in the picture, on opposite sides of the hole's shadow. Can you recognize any pairs? The shadow of the black hole in the picture is made up of directions from which no ray can reach the camera; look at the triangular area labeled "shadow" in the top diagram. All the rays that "want to be" in the shadow are caught and swallowed by the black hole.

As the camera moves to the right in the orbit (Figure 8.3), the star pattern seen by the camera changes as shown in Figure 8.4.

In this figure, two separate stars are highlighted. One is circled in red (the same star is circled in Figure 8.3). The other is inside the yellow marker. We see two images of each star: one outside the pink circle, the other inside. The pink circle is called "Einstein's ring".

As the camera moves to the right, the images move along the red and yellow curves.

The images of stars outside the Einstein ring (let's call them primary images) move as you would expect: smoothly from left to right, but leaning away from the black hole as they move. (Can you explain why the deviation occurs from holes, and not to it?)

Rice. 8.4. Change in the star pattern seen by the camera as it orbits to the right in Figure 8.3. [Modeled by Alain Riazuelo; see www2.iap.fr/users/riazuelo/interstellar.]

However, the secondary images, inside the Einstein ring, move in an unexpected way: they seem to emerge from the right edge of the shadow, move outward into the ring between the shadow and the Einstein ring, rotate around the shadow, and descend again to the edge of the shadow. This can be understood by returning to the top picture in figure 8.3. The right beam passes close to the black hole, so the right image of the star is close to its shadow. At an earlier point in time, when the camera was to the left, the right ray had to go even closer to the black hole in order to bend more and get to the camera, so the right image was very close to the edge of the shadow. In contrast, at an earlier point in time, the left ray passed quite far from the hole, so that it was almost straight and produced an image quite far from the shadow.

Now, if you're ready, think about the subsequent movement of the images, captured in Figure 8.4.

Rapidly Spinning Black Hole Lens: Gargantua

The spatial vortex created by Gargantua's rapid rotation changes the gravitational lens. The star patterns in Figure 8.1 (Gargantua) look slightly different than those in Figure 8.4 (non-rotating black hole), and the streaming patterns are even more different.

In Gargantua's case, the jet (Figure 8.5) reveals two Einstein rings, shown as pink curves. Outside the outer ring, the stars stream to the right (for example, along the two red curves), as in the case of the non-rotating black hole in Figure 8.4. However, the spatial vortex has concentrated the flowing stream into narrow high-velocity bands along the trailing edge of the hole's shadow, curving sharply near the equator. The vortex also created turbulences in the jet (closed red curves).

The secondary image of each star is visible between two Einstein rings. Each secondary image rotates along a closed curve (for example, two yellow curves), and it rotates in the opposite direction to the red streaming movement outside of the outer ring.

Rice. 8.5. Drawing of a stellar jet as seen by a camera next to a rapidly spinning black hole like Gargantua. In this Double Negative visual effects team model, the hole rotates at 99.9 percent of its maximum possible speed, and the camera is in a circular equatorial orbit with a circumference six times the circumference of the horizon. See a video of this model on this book's page at Interstellar.withgoogle.com.

There are two very special stars in Gargantua's sky with the gravitational lens turned off. One lies just above Gargantua's north pole, the other just below its south pole. These are analogues of the North Star, which is located exactly above the north pole of the Earth. I have placed five-pointed stars on the primary (red) and secondary (yellow) images of Gargantua's pole stars. All the stars in Earth's sky seem to revolve around Polaris as we are being pulled around by the Earth's rotation. Similarly, in Gargantua, all primary star images revolve around the red images of the pole stars as the camera moves around the hole, but their reversal trajectories (for example, two red turbulence curves) are strongly distorted by the spatial vortex and the gravitational lens. Similarly, all secondary star images revolve around the yellow polar star images (eg, along two distorted yellow curves).

Why, in the case of a non-rotating black hole (Figure 8.4), was it seen that the secondary images emerge from the black hole's shadow, rotate around the hole, and descend back into the shadow, rather than revolve around in a closed curve, as in Gargantua's case (Figure 8.5)? Actually, they are apply along a closed curve in the case of a non-rotating black hole. However, the inner edge of this closed curve is so close to the edge of the shadow that it cannot be seen. Gargantua's rotation creates a spatial vortex, and this vortex pushes Einstein's inner ring outward, revealing the drawing. full circulation secondary images (yellow curves in Figure 8.5) and the inner Einstein ring.

Inside the inner Einstein ring, the jet pattern is more intricate. The stars in this region are tertiary and even higher-order images of all the stars in the universe - the same ones seen as primary images outside of the outer Einstein ring and as secondary images between the Einstein rings.

In Figure 8.6, I show five small pictures of Gargantua's equatorial plane, with Gargantua itself in black, the camera's orbit in pink dotted lines, and the beam of light in red. The beam of light carries the image of a star to the camera, which is located at the tip of the blue arrow. The camera moves around Gargantua counterclockwise.

You can really get into the gravitational lens if you walk through these pictures one by one on your own. Note that the true direction to the star is up and to the right (look at the outer ends of the red rays). The camera and the beginning of each beam points to the image of the star. The tenth image is very near the left edge of the shadow, and the right secondary image is near the right edge; comparing the camera directions for these images, we can see that the shadow spans an arc of about 150 degrees in the upward direction. This is despite the fact that the actual direction from the camera to the center of Gargantua is to the left and up. The lens shifted the shadow relative to Gargantua's present position.

Rice. 8.6. Rays of light that carry images of stars at the tips of the blue arrows. (English primary - primary, secondary - secondary, tertiary - tertiary.) [From the same Double Negative model as in figures 8.1 and 8.5.]

Creating Black Hole and Wormhole Visual Effects in Interstellar

Chris wanted Gargantua to look like in fact looks like a rapidly spinning black hole up close, so he asked Paul to consult me. Paul put me in touch with the team Interstellar, which he assembled at Double Negative's visual effects studio in London.

I got into a frenzy working closely with Oliver James, the chief scientist. Oliver and I talked on the phone and Skype, exchanged emails and files, and met in person in Los Angeles and at his office in London. Oliver has degrees in optics and atomic physics and understands Einstein's laws of relativity, so we spoke the same technical language.

Some of my fellow physicists have already done computer models what an observer would see while orbiting a black hole, or even falling into it. The best judges were Alain Riazuelo from the Institut d'Astrophysique in Paris and Andrew Hamilton at the University of Colorado at Boulder. Andrew created a video about black holes that is shown in planetariums around the world, and Alain has modeled black holes that spin very, very fast, like Gargantua.

So my original intention was to set Oliver up with Alain and Andrew and ask them to provide him with the required input. For several days I was uncomfortable with this decision, and then I changed my mind.

During my half-century career as a physicist, I made great efforts, making new discoveries myself and educating students who made new discoveries. Why not, for a change, do something just because it's fun, I asked myself, even if others have done it before me? So I lashed out at that "something". And it was fun. And to my surprise, as a by-product it led (modestly) to new discoveries.

Using the laws of relativity and drawing heavily on the work of predecessors (notably Brandon Carter at Laboratoire Univers et Théories in France and Jeanne Levine at Columbia University), I deduced the equations Oliver needed. These equations calculate the paths of light rays starting from some source of light, such as a distant star, and moving through Gargantua's curved space towards the camera. From these rays of light, my equations then calculate the images seen by the camera, taking into account not only the light sources and Gargantua's space and time distortion, but also the movement of the camera around the Gargantua.

Having obtained these equations, I tried them myself with the help of a friendly software called Mathematica. I compared the images generated by my Mathematica computer code with those of Alain Riazuelo, and when they agreed, I rejoiced. I then wrote detailed descriptions of my equations and sent them to Oliver in London, along with my Mathematica code.

My code was very slow and low resolution. Oliver's task was to translate my equations into computer code that could produce the ultra-high quality IMAX images needed for the film.

Oliver and I did it step by step. We started with a non-rotating black hole and a stationary camera. Then we added the rotation of the black hole. Then we added camera movement: first moving in a circular orbit, and then falling into a black hole. And then we switched to a camera revolving around a wormhole.

At this point Oliver struck me like a thunderbolt in the midst of clear sky: to model the most subtle effects, he would need not only equations describing the paths of light rays, but also equations describing how the cross section of a beam of light changes size and shape as it passes through a wormhole.

I more or less knew how to do it, but the equations were terribly confusing and I was afraid of making mistakes. So I searched the technical literature, and found that in 1977 Serge Pineault and Rob Rouber of the University of Toronto got the necessary equations in almost the form I needed. After three weeks of wrestling with my own stupidity, I reshaped their equations in exactly the right form, expressed them in Mathematica, and painted them for Oliver, who incorporated them into his own computer code. After all, his code was able to produce the quality images needed for the film.

In Double Negative, Oliver's computer code was just the beginning. He handed it to the art team, led by Eugenia von Tanzelmann, who added an accretion disk (Chapter 9) and created a background galaxy with stars and nebulae that would be distorted by the Gargantua lens. Her team then added Endurance, Rangers and landers and camera animations (changing movement, direction, field of view, etc.) and molded the images into very convincing forms: into incredible scenes that appear in the film. Continued in Chapter 9 .

In the meantime, I've been racking my brains over the high-quality videos Oliver and Evgenia have sent me, trying hard to figure out why the images look the way they do, and the starfields flow the way they do. For me, these videos are like experimental data: they reveal things that I would never have figured out on my own, without these models - for example, what I described in the previous section (Figures 8.5 and 8.6). We are going to publish a technical article or two describing what we have learned.

Appearance of Gravity Slings

Although Chris chose not to show any of the gravity slings in Interstellar, I wondered what they would have looked like to Cooper as he led the Ranger to Miller's planet. So I used my equations and Mathematica to model the images. (My images have a much lower resolution than Oliver and Eugenia's due to the slowness of my code.)

Figure 8.7 shows a series of images seen from Ranger Cooper as it loops around a black hole. medium weight(CHDSM) to start the descent to Miller's planet - in my scientific interpretation Interstellar. This is the sling described in figure 7.2.

Figure 8.7. Gravity sling around the CHDSM with Gargantua in the background [My own model and rendering.]

In the top image, Gargantua is at the back with the HRSM passing in front of her. The CHDSM captures rays of light from distant stars directed towards Gargantua, scrolls them around itself and throws them towards the camera. This explains the donut of starlight surrounding the shadow of the CHDSM. Although the HRSM is a thousand times smaller than Gargantua, it is much closer to Ranger than Gargantua, so it looks only moderately smaller.

As the PRSM moves to the right for the sling-moving camera, it leaves behind the primary shadow of Gargantua (the middle picture in Figure 8.7), and pushes the secondary image of Gargantua's shadow in front of it. These two images are completely analogous to the primary and secondary images of a star refracted by the gravitational lens of a black hole; but now the PDSM lens refracts Gargantua's shadow. In the bottom image, the size of the secondary shadow is shrinking as the PDSM moves further. At this point, the gravity sling is nearly complete, and the camera aboard the Ranger zooms down to Miller's planet.

Impressive as these images are, they can only be seen close to the CHDSM and Gargantua, and not from a great distance to the Earth. For terrestrial astronomers, the most impressive optical effects of giant black holes are the jets protruding from them and the light from the sparkling disk of gas in their orbit. We will now turn to them.

A black hole arises as a result of the collapse of a supermassive star, the core of which runs out of "fuel" for a nuclear reaction. As the core contracts, the temperature of the core rises, and photons with an energy of more than 511 keV, colliding, form electron-positron pairs, which leads to a catastrophic decrease in pressure and further collapse of the star under the influence of its own gravity.

Astrophysicist Ethan Siegel published the article "The Largest Black Hole in the Known Universe" in which he collected information about the mass of black holes in different galaxies. Just wondering: where is the most massive of them?

Since the densest clusters of stars are in the center of galaxies, now almost every galaxy has a massive black hole in the center, formed after the merger of many others. For example, in the center milky way there is a black hole with a mass of about 0.1% of our galaxy, that is, 4 million times the mass of the Sun.

It is very easy to determine the presence of a black hole by studying the trajectory of the movement of stars, which are affected by the gravity of an invisible body.

But the Milky Way is a relatively small galaxy that cannot possibly have the largest black hole. For example, not far from us in the Virgo cluster is the giant galaxy Messier 87 - it is about 200 times larger than ours.

So, a stream of matter about 5000 light years long breaks out from the center of this galaxy (pictured). It's a crazy anomaly, writes Ethan Siegel, but it looks very nice.

Scientists believe that the only explanation for such an "eruption" from the center of the galaxy can be a black hole. The calculation shows that the mass of this black hole is about 1500 times greater than the mass of a black hole in the Milky Way, that is, approximately 6.6 billion solar masses.

But where is the largest black hole in the universe? If we proceed from the calculation that in the center of almost every galaxy there is such an object with a mass of 0.1% of the mass of the galaxy, then we need to find the most massive galaxy. Scientists can answer this question too.

The most massive galaxy known to us is IC 1101 at the center of the Abell 2029 cluster, which is 20 times further from the Milky Way than the Virgo cluster.

In IC 1101, the distance from the center to the farthest edge is about 2 million light years. Its size is twice as large as the distance from the Milky Way to our nearest galaxy, Andromeda. The mass is almost equal to the mass of the entire cluster of Virgo!

If there is a black hole at the center of IC 1101 (and there should be), then it could be the most massive in the known Universe.

Ethan Siegel says he could be wrong. The reason is the unique galaxy NGC 1277. This is not a very large galaxy, slightly smaller than ours. But the analysis of its rotation showed an incredible result: the black hole in the center is 17 billion solar masses, and this is already 17% of the total mass of the galaxy. This is a record for the ratio of the mass of a black hole to the mass of a galaxy.

There is another candidate for the role of the largest black hole in known universe. It is shown in the next photo.

The strange object OJ 287 is called a blazar. Blazars are a special class of extragalactic objects, a kind of quasars. They are distinguished by very powerful radiation, which in OJ 287 changes with a cycle of 11-12 years (with a double peak).

According to astrophysicists, OJ 287 includes a supermassive central black hole orbiting another smaller black hole. At 18 billion solar masses, the central black hole is the largest known to date.

This pair of black holes will be one of the best experiments to test the general theory of relativity, namely the deformation of space-time, described in general relativity.

Due to relativistic effects, the perihelion of the black hole, that is, the point of the orbit closest to the center black hole, must move 39° per revolution! By comparison, Mercury's perihelion has shifted by only 43 arcseconds per century.

Some of what is shown in the film is pure truth, some is based on scientific assumptions, and some is pure speculation.

Christopher Nolan's film "Interstellar" is called by many the most scientific in modern science fiction, but claims are made against him in all severity. Disputes about the merits and demerits of this picture make people bury their heads in physics textbooks. Let's try and figure out how Interstellar became what it is, and what is strictly scientific in it, and what is not quite.

CAREFULLY! SPOILERS!

Video version of this article.

The Man Who Invented Interstellar

The name of the famous physicist Kip Thorne pops up in every debate about the scientific nature of Nolan's painting. The scientist played a huge role in making the film. Thorne was not limited to the role of a scientific consultant - in fact, it was he who came up with Interstellar.

Profile: Stephen Kip Thorne

Specialist in the theory of gravity, astrophysics and quantum theory of measurements. For more than fifteen years he was a professor at the California Institute of Technology (Caltech). One of the world's leading experts on general relativity. Popularizer of science. Close friend and colleague of Stephen Hawking.

About thirty years ago, the famous Stephen Hawking arranged for his friend, young physicist and single father Kip Thorne, a blind date with Linda Obst, science editor of The New-York Times Magazine and aspiring television producer. The couple did not have a romance, but a strong friendship was formed. Ten years ago, Linda and Kip had the idea to create a film based on achievement and knowledge. modern science. They wrote an eight-page sketch, which featured, among other things, as many as six wormholes, five black holes and a mysterious race of aliens living in a "beam" - a space that has at least five dimensions. One of the heroes was supposed to be Stephen Hawking, who personally went into space.

Offering his idea to the film studio, Thorne set a condition: all plot moves in the film must be scientifically reliable, or at least based on acceptable theories and speculation.

The Paramount studio became interested in the idea, and Steven Spielberg himself sat in the director's chair. The script was given to Christopher Nolan's younger brother Jonathan. But then difficulties began: due to the Writers Guild strike, John stopped working on the film, then he had to switch to The Dark Knight, and Spielberg did not share something with the Paramount bosses and left the project. Thorne lost heart, but Linda did not despair and in a couple of weeks she found a new director - Christopher Nolan.

The elder Nolan brought a lot of new things to Interstellar. Chris rewrote the script, combining it with his own ideas, originally intended for a completely different project. The final draft was nothing like the original eight-page draft, but Kip was not upset because, from his point of view, Nolan almost always adhered to the principle voiced by Thorne. Thorne categorically objected to the director only once - when Chris came up with a scene where the characters were moving faster than light. Kip spent two weeks arguing why it was completely impossible, and got his way.

At the same time, Kip understood that Chris was making a feature film, so he turned a blind eye to the small inaccuracies needed to enhance the drama, and only made sure that Nolan's fantasy did not take too far. Did he succeed? Let's figure it out.

Dusty world and pathogens

The beginning of Interstellar takes place on the Earth of the future, which looks extremely unattractive. A new pathogen has wiped out all crops except corn, starvation has threatened, governments have disbanded their armies and scientific centers, a simple people forced to become farmers to feed themselves. As if that weren't enough, residents suffer from regular dust storms that have turned most of the US into a "dust pot". Worse than that, the pathogen destroys the supply of oxygen in the air, replacing it with nitrogen, so that those who do not die of hunger will simply suffocate.

CLAIM: Wait! How could a single pathogen wipe out all plant life? As a rule, such things only affect certain types of plants, completely wiping out their population. The same diseases that affect several species at once, as a rule, are not so strong.

The history of the Earth knows examples of mass extinctions, when most of the living beings died due to drastically changed conditions. This happened when cyanobacteria arose, releasing oxygen, which in those days was a real poison for most species. Now a similar microorganism may well develop, which, for example, will release nitrogen into the atmosphere.

There is another possible scenario: the emergence of a new disease that affects the main varieties of plants on which we depend most. Biologists do not exclude such a possibility, although they find it extremely unlikely.

COUNTERARGUMENT: But why, in such a situation, cut spending on science? They, on the contrary, must be increased so that biologists develop new plant cultures that are immune to the virus, invent a vaccine, an antidote, or another way to deal with scourge. After all, this is how we are now fighting any disease that has even the slightest chance of causing a pandemic. Among other things, this is a giant business where you can earn a lot of money. Much more profitable than growing corn in Kansas.

Perhaps there were such attempts, but they failed. Even now there are diseases for which vaccines have not yet been found, although development has been underway for thirty years. Suppose, at first, the states really spent hundreds of millions on the search for a cure, but then the revenues to the treasury stopped, the budgets dried up, and funding had to be canceled.

COUNTERARGUMENT: But where does oxygen go from the air?

Oxygen in the atmosphere mainly comes from plant photosynthesis. If a new pathogen affects precisely this process, oxygen will no longer be a renewable resource. Now let's see how carbon dioxide is formed: either in the process of respiration of all living beings, or as a result of decay of organic matter, or in the form industrial emissions enterprises and vehicle emissions. Even if, after famine and the economic crisis, the population decreases and emissions into the atmosphere decrease, the dying vegetation will rot in the fields. According to some estimates, about a percent of the remaining oxygen reserves will be consumed during the decay process. Will take his place carbon monoxide, which will make breathing difficult for sensitive people and raise the air temperature by ten degrees. Not fatal, of course, but pleasant enough.

However, it must be admitted that such a scenario is unlikely. It is used in the film not as a prediction of the future, but as a plot twist designed to force the characters to go into space.

Wormhole and Endurance

Taking advantage of a successfully turned up wormhole, NASA equips an interstellar expedition on the Endurance spacecraft in search of a new home for mankind. It's good that there is a hole near Saturn! Indeed, in Cooper's world, travel at the speed of light is impossible, and it would take thousands of years to fly to the stars.

CLAIM: Are wormholes real? Have physicists registered at least one?

No, but science admits their existence, or at least does not deny it. And what is not forbidden ... Recently, not without the participation of Mr. Thorne, the idea is gaining popularity in cosmology that space is not an endless void, but a kind of material that can be changed if there were the right tools.

COUNTERARGUMENT: Let's say. But to maintain a hole in working order, considerable amounts of negative or exotic matter are required. Yes, and opening a hole requires a source of huge gravity such as Gargantua, and the appearance of such in the solar system would plunge it into chaos.

And even if a wormhole were to appear - for example, due to the influence of Gargantua - it would be a one-way road. The return journey would require a similar source of gravity from the other side.

Yes, the very appearance of a hole is a necessary license. In the movie, the characters assumed that the wormhole was created by creatures living in 5D space to show us the way to salvation.

COUNTERARGUMENT: Professor Brand says that the wormhole appeared in the orbit of Saturn fifty years before the events of Interstellar. NASA was dispersed ten years before the start of the film. That is, for forty years no one knew anything about the appearance of a gravitational anomaly within solar system? Yes, crowds of string theorists would have lined up at the Nobel Committee. This is the news of the century!

Half a century has passed since then, everyone managed to forget about some hole in space - there were enough problems. Only one crazy grandfather remembers her, who lives underground, mows under Kip Thorne and collects spaceships on the knee.

CLAIM: Speaking of the ship! Why did the booster put him into orbit if he was able to take off from the planets Miller and Manna?

Firstly, the Endurance went into orbit, and the astronauts landed on the planets in the Ranger, a shuttle docked to the Endurance. Secondly, there are no gas stations on the way from Earth to Gargantua, so fuel must be saved.

COUNTERARGUMENT: Speaking of fuel. A lot of it is required for such a journey. Why don't we see giant fuel tanks in any frame from the Endurance?

Are you sure that the camera showed all the compartments? Why, for example, show cargo holds where nothing happens? In addition, on the way to Saturn, the members of the expedition could save fuel with the help of gravity maneuvers - accelerate, slow down or change the direction of flight under the influence of gravity. celestial bodies. This is how NASA launched the Cassini probe in the late 1990s. There was not enough fuel on board to get to Saturn, but NASA calculated the course so that Cassini would pass on the tangent of the orbits of Venus, Earth and Jupiter. Each such maneuver gave the probe acceleration.

To get from Earth to Saturn in two years, the Endurance must cover an average of 20 kilometers per second. Kip Thorne believes that with the help of maneuvers and increasing the efficiency of rocket fuel, by the end of the 21st century, humanity will be able to reach speeds of 300 kilometers per second. So flying to Saturn in such a time is quite realistic.

COUNTERARGUMENT: But how did they slow down in the orbit of Saturn and not fly further? The power of the ship's bow engines would clearly not be enough here.

On their own, perhaps, it would not be enough, but with the help of regular course corrections in the orbit of Saturn - why not? In addition, do not forget about the wormhole, which could well affect the location of gravitational fields.

Life orbiting a black hole

After passing through a wormhole, Cooper and the others find themselves at the end point of their journey - a planetary system near the huge black hole Gargantua. This celestial body is a source of special pride for both Kip Thorne and the special effects masters. When depicting the hole, calculations made by Thorne specifically for the film were used. The result stunned Kip himself. He guessed how black holes should look in reality, but the computer animation exceeded all his expectations.

CLAIM: No other celestial bodies are visible near Gargantua, except for a couple of planets. Where do the planets of Miller, Edmunds and Mann draw heat and light from?

From the accretion disk. Gargantua's gravity is so strong that it can capture an entire star. When a star moves straight into a black hole, its fate is deplorable and predictable. If its orbit lies next to Gargantua, then the attraction of the black hole simply tears the celestial body apart, and most of the matter that previously made up the star's body falls into Gargantua's orbit and forms an accretion disk. It emits light, heat, and radiation, so it could well replace the sun.

COUNTERARGUMENT: It turns out that it is impossible to live on these planets because of high temperatures and radiation. How did the crew of the Endurance not get fried just by flying by?

Perhaps several million years have passed since the last star fell into the gravitational grip of Gargantua. Then the gas that makes up the disk has cooled to a temperature of several thousand degrees and no longer emits such strong radiation, although it continues to give enough light and heat. The low temperature also explains the fading of the disk.

Gargantua is the most authentic black hole in the history of cinema. But even it is different from reality.

CLAIM: Where did the planets come from? Shouldn't they have been sucked into the hole?

In fact, science admits the existence of zones of ordinary time and space near giant black holes, even entire planetary systems that revolve around the central singularity in complex but closed orbits.

CLAIM: The accretion disk looks implausible. It should be somewhat flattened and asymmetrical. In addition, the model does not take into account the Doppler effect: one edge of the disk should be red, the other blue.

Yes, here Christopher Nolan deliberately went against the truth so as not to embarrass the audience. And he deliberately underestimated the speed of rotation of the black hole. In addition, given the distance from the black hole to the planet Miller, Gargantua should occupy half the sky, and the planet in this scenario would be inside the accretion disk, so it would mostly be visible only from the side of the planet opposite the hole.

Planets Miller and Manna

First of all, the astronauts go to the planet Miller. Time there goes slowly - one hour on its surface is equal to seven Earth years.

CLAIM: This is possible only near objects with a huge mass, for example, in the orbit of a black hole. But you need to be very close to the hole, almost above its surface. And a stable orbit around a black hole must be at least three times the diameter of Gargantua. Otherwise, Miller's planet would have been sucked in a long time ago. Taking into account the frames shown in the film, time on the surface of the planet should flow more slowly than on Earth, by only twenty percent.

This is true of non-rotating black holes, but with Gargantua, things are different. Gargantua is a supermassive rotating black hole, which somewhat changes its effect on the surrounding space. Under certain conditions, say, if it rotates very quickly, and the planet Miller is located close enough to Gargantua's circular orbit, such a time dilation is possible.

True, rotating black holes have a limit on the speed of rotation, and, as a rule, they do not reach a maximum. For the planet Miller to have such a time dilation, Gargantua would have to rotate only a little less than the maximum. This is real, although unlikely.

COUNTERARGUMENT: What about tidal waves? They are possible only if the difference in the gravitational pull of the black hole is different sides the planet is very large. But in this case, the planet would simply be torn apart!

Not really. Due to the gigantic size of Gargantua, the difference in the attraction of the black hole on different sides of the Miller planet is not large enough. Nevertheless, the force of gravity should have been enough to deform the planet. Miller's planet was supposed to look like an ellipsoid, compressed on the sides and elongated in length. In addition, if the planet rotated around its axis, then Gargantua's attractive forces would act in several directions, depending on the position of the orbits. In the film, we see that all giant waves move in approximately the same direction. From this follows the conclusion that the planet Miller is always turned to the black hole by the same side.

Another explanation is also possible: due to the deformation of the planet and the attraction of Gargantua, earthquakes constantly occur in certain areas, causing giant tsunamis.

COUNTERARGUMENT: Radiation, absence of the usual source of light and heat - the planet Miller does not look like a suitable place to live. Was it really necessary to fly to it in the first place, and was it really impossible to avoid this part of the expedition?

Of course it was possible. The planet Miller would never have become the first candidate for a new home for humanity if Cooper or other members of the Endurance crew had guessed to use for their intended purpose a bunch of scientific equipment that was brought aboard the ship for this purpose. Information about the suitability of the planet Miller for life could be obtained directly from orbit using telescopes and other instruments. The same ones that Romilly studied the black hole itself for almost a quarter of a century, while the rest fought the tsunami.

Without descending to the planet, it would be possible to study it from a safe distance, where the time lag is minimal. Simple spectral analysis it would be great to save the fuel of the expedition and reduce the intensity of passions on the screen. Christopher Nolan needed this time dilation to show how the gap between father and daughter is growing.

As a last resort, if NASA really wanted to send a delegation of thinking beings to the planet, it would be quite possible to send a crew consisting of only robots to the expedition. Robots are able to survive in almost any conditions (judging by the film - even in a black hole), they are less demanding, not so capricious and endure loneliness more easily.

CLAIM: How justified are Cooper's maneuvers before landing on the planet Miller to avoid time dilation and the pull of a black hole?

In any case, he would not have avoided the slowdown of time - it increases inversely with the distance from the black hole. But save time by correcting the course of the ship due to the gravitational attraction of different celestial bodies as much as possible. In the film, Cooper decides to avoid Gargantua's pull by accelerating to great speed and then braking hard, hitting the neutron star's gravitational pull.

In fact, it would not have been possible to reduce speed in this way (and so that the ship and passengers would not be torn to pieces during sudden braking) with the help of a neutron star - this requires a small black hole the size of the Earth. But Nolan was adamant about the number of black holes in the film: one, only one!

***

Fast forward to the planet Manna. The action takes place high above the surface, in the sky of which giant ice clouds hang.

CLAIM: How is it possible for such clouds to exist? And why don't they fall under their own weight?

Apparently, the planet Manna revolves around Gargantua in an extremely complex orbit and spends most of the time away from the black hole. Why? First, it was almost the longest flight to the planet Mann when the crew of the Endurance decided where to start. But when Cooper takes off from the planet, the Ranger is very close to Gargantua. And secondly, this is hinted at by giant ice clouds that freeze for the time that the planet is removed from the accretion disk.

And they do not fall thanks to a special kind of magic. Film magic. In fact, they should have collapsed to the surface long ago.

Fall into a black hole

CLAIM: After taking off from Mann's planet, the Endurance is gripped by Gargantua's gravity. Cooper manages to save the main module, but he, the TARS robot and the Ranger pass through the event horizon and fall into a black hole. How did they survive the whole process? They should have either been killed by the radiation and temperature of the accretion disk, or they should have been spaghettified - turned into an elongated thread due to the difference in the attraction of different parts of the body.

If Gargantua last captured the stars in her gravitational trap millions of years ago, then the disk became safe for casual travelers (and useless for the surrounding planets, by the way). As for spaghettification, it is again possible in small and non-rotating black holes. The size and speed of rotation of Gargantua reduce the difference in attraction various parts bodies to zero, so there is no need to fear turning into spaghetti.

COUNTERARGUMENT: Does this mean that one can safely survive falling into a black hole?

Of course not. Going after TARS, Cooper signed his own death warrant and he knew it himself.

COUNTERARGUMENT: Suppose, by some miracle, Cooper survived. How did he expect to transmit the signal back home? After all, they experienced difficulties even with signal transmission through a wormhole. What can we say about a black hole, from which, as you know, nothing escapes.

It was believed that nothing, not even light, could escape the attraction of a black hole. But Stephen Hawking proved that black holes can also radiate elementary particles, mostly photons. Some theories imply that information is basically unstoppable, but there is no consensus among scientists on this issue. However, they are unlikely to agree that a signal can be broadcast from a black hole, so this is, of course, an exaggeration.

CLAIM: What is this gravitational data, without which it is impossible to solve the equation of Professor Brand?

According to the film, the professor needed the data to help him understand gravity and how it interacts with quantum mechanics. Subsequently, this would help raise new human colonies from the Earth. Of course, in order to solve such problems in real life jumping into a black hole is not needed. And it is unlikely that such data can be transmitted in such a short sequence of signals.

CLAIM: After passing the event horizon, Cooper finds himself in a tesseract, a four-dimensional hypercube that allows you to measure time as a linear quantity and allows you to communicate with Murph at any point in her life. Is that also scientific?

From the moment of the jump into the black hole until the end of the film, the script ceases to focus on science and operates on pure speculation. Yes, scientists admit the existence of other dimensions, but their knowledge in three-dimensional space is not possible. And of course, it is impossible to scientifically prove that after jumping into a black hole, unknown forces will transfer a person to his daughter's room. All these mysterious phenomena Nolan writes off on the mysterious and mysterious "them" living in five-dimensional space.

***
Nolan was filming science fiction after all, not documentaries, so he had the right to ignore some details. Interstellar was sometimes the victim of artistic design, visual solutions were made for the convenience of the audience and the film crew, and not for scientists. Nevertheless, the picture turned out to be much more scientific than most modern science fiction. Think about it: in what other session did we even need to know how real astrophysics works?

Black holes don't emit light, so the only way to see Gargantua is through its effect on light from other objects. AT Interstellar other objects are the accretion disk () and the galaxy in which it resides, including nebulae and an abundant star field. For the sake of simplicity, let's include only the stars for now.

Gargantua casts a black shadow on the star field, and also refracts the rays of light from each star, distorting the star pattern visible to the camera. This distortion is the gravitational lens described in .

Figure 8.1 shows a rapidly spinning black hole (let's call it Gargantua) in front of a star field as it would appear to you if you were in Gargantua's equatorial plane. The Shadow of Gargantua is a completely black area. Just beyond the edge of the shadow is a very thin ring of starlight, the so-called "ring of fire", which I manually enhanced to make the edge of the shadow more defined. Outside the ring, we see a thick spray of stars in a concentric pattern created by a gravitational lens.

Rice. 8.1. A stellar pattern created by a gravitational lens around a rapidly spinning black hole like Gargantua. Seen from afar, the angular diameter of the shadow in radians is 9 Gargantua radii divided by the distance from the observer to Gargantua. [Modeled for this book by the visual effects team at Double Negative.]

As the camera moves along Gargantua's orbit, the stars appear to be moving. This movement, combined with the lens, creates spectacularly changing light patterns. In some regions, the stars stream with great speed, in others they flow calmly, in still others they freeze in place; see the video on this book's page at Interstellar.withgoogle.com.

In this chapter, I explain all these nuances, starting with the shadow and its ring of fire. Later I will describe how the images of the black hole were actually obtained in Interstellar.

In portraying Gargantua in this chapter, I consider it to be a rapidly spinning black hole, which is what it should be in order to provide an extreme loss of crew time. Endurance in relation to the Earth (). However, in the case of fast rotation, the flattened left edge of Gargantua's shadow (Figure 8.1) and some specific features of the stellar jet and accretion disk could be confused by a mass audience, so Christopher Nolan and Paul Franklin chose a slower rotation speed - 60 percent of the maximum - for images of Gargantua in the film. See the last section in .

Warning: The explanations in the next three sections may require a lot of mental effort; they can be skipped without losing the thread of the rest of the book. Don't worry!

The Shadow and Her Ring of Fire

Let's say you are at the yellow dot. white rays A and B, as well as other rays like them, bring you the image of a fiery ring, and black rays A and B bear the image of the edge of the shadow. For example, a white beam A emanating from some star far from Gargantua, it moves inwards and is trapped along the inner edge of the shell of fire in the equatorial plane of Gargantua, where it flies around again and again, driven by a vortex of space, and then escapes and reaches your eyes. Black beam, also signed A, comes from Gargantua's event horizon, it moves outward and gets trapped on the same inner edge of the fire shell, then escapes and reaches your eyes side by side with the white beam A. The white beam carries the image of a piece of a thin ring, and the black one - the image of a piece of the edge of the shadow. The fiery shell is responsible for bringing them side to side and directing them into your eyes.

Rice. 8.2. Gargantua ( sphere in the center), its equatorial plane ( blue), fireshell ( pink and purple) and black and white rays, carrying the image of the edge of the shadow and a thin ring around it.

Similarly for white and black rays B, only they fall into a trap on the outer edge of the shell of fire and move clockwise (making their way towards the spatial vortex), while the rays A get trapped on the inner boundary and move counterclockwise (and the dimensional whirlwind picks them up). In figure 8.1, the left edge of the shadow is flattened, and the right edge is rounded due to the fact that the rays A(from the left edge) come from the inner border of the shell of fire, very close to the horizon, and the rays B(from the left edge) - from the outside, located much further from the horizon.

black rays C and D in figure 8.2 originate at the horizon, move outward and are trapped in non-equatorial orbits in a shell of fire, then escape their trap orbits and reach your eyes, carrying images of bits of the edge of the shadow that lie outside the equatorial plane. Beam Trap Orbit D shown in the top right inset. white rays FROM and D(not shown) coming from distant stars are trapped side by side with black beams C and D and move towards your eyes side by side with C and D, carrying images of fire ring pieces side by side with shadow edge pieces.

The lens of a non-rotating black hole

To understand the pattern of stars refracted by a gravitational lens and their jet as the camera moves, let's start with a non-rotating black hole and with rays of light emanating from a single star (Figure 8.3). Two beams of light go from the star to the camera. Each one travels in the straightest path it can in the curved space of the hole, but the curvature causes each beam to bend.

One curved beam moves towards the camera around the left edge of the shadow, the other around its right edge. Each beam carries its own image of the star to the camera. These two images as seen by the camera are shown in the inset in Figure 8.3. I circled them with red circles to distinguish them from all the other stars seen by the camera. Note that the right image is much closer to the hole's shadow than the left image. This is because its curved beam traveled closer to the hole's event horizon.

Rice. 8.3. Above: The curved space of a non-rotating black hole as seen from the bulk, and two beams of light moving through the curved space from the star to the camera. Bottom: A stellar pattern refracted by a gravitational lens as seen by a camera. [Modeled by Alain Riazuelo; see the video of his model at www2.iap.fr/users/riazuelo/interstellar.]

Every other star appears twice in the picture, on opposite sides of the hole's shadow. Can you recognize any pairs? The shadow of the black hole in the picture is made up of directions from which no ray can reach the camera; look at the triangular area labeled "shadow" in the top diagram. All the rays that "want to be" in the shadow are caught and swallowed by the black hole.

As the camera moves to the right in the orbit (Figure 8.3), the star pattern seen by the camera changes as shown in Figure 8.4.

In this figure, two separate stars are highlighted. One is circled in red (the same star is circled in Figure 8.3). The other is inside the yellow marker. We see two images of each star: one outside the pink circle, the other inside. The pink circle is called "Einstein's ring".

As the camera moves to the right, the images move along the red and yellow curves.

The images of stars outside the Einstein ring (let's call them primary images) move as you would expect: smoothly from left to right, but leaning away from the black hole as they move. (Can you explain why the deviation occurs from holes, and not to it?)

Rice. 8.4. Change in the star pattern seen by the camera as it orbits to the right in Figure 8.3. [Modeled by Alain Riazuelo; see www2.iap.fr/users/riazuelo/interstellar.]

However, the secondary images, inside the Einstein ring, move in an unexpected way: they seem to emerge from the right edge of the shadow, move outward into the ring between the shadow and the Einstein ring, rotate around the shadow, and descend again to the edge of the shadow. This can be understood by returning to the top picture in figure 8.3. The right beam passes close to the black hole, so the right image of the star is close to its shadow. At an earlier point in time, when the camera was to the left, the right ray had to go even closer to the black hole in order to bend more and get to the camera, so the right image was very close to the edge of the shadow. In contrast, at an earlier point in time, the left ray passed quite far from the hole, so that it was almost straight and produced an image quite far from the shadow.

Now, if you're ready, think about the subsequent movement of the images, captured in Figure 8.4.

Rapidly Spinning Black Hole Lens: Gargantua

The spatial vortex created by Gargantua's rapid rotation changes the gravitational lens. The star patterns in Figure 8.1 (Gargantua) look slightly different than those in Figure 8.4 (non-rotating black hole), and the streaming patterns are even more different.

In Gargantua's case, the jet (Figure 8.5) reveals two Einstein rings, shown as pink curves. Outside the outer ring, the stars stream to the right (for example, along the two red curves), as in the case of the non-rotating black hole in Figure 8.4. However, the spatial vortex has concentrated the flowing stream into narrow high-velocity bands along the trailing edge of the hole's shadow, curving sharply near the equator. The vortex also created turbulences in the jet (closed red curves).

The secondary image of each star is visible between two Einstein rings. Each secondary image rotates along a closed curve (for example, two yellow curves), and it rotates in the opposite direction to the red streaming movement outside of the outer ring.

Rice. 8.5. Drawing of a stellar jet as seen by a camera next to a rapidly spinning black hole like Gargantua. In this Double Negative visual effects team model, the hole rotates at 99.9 percent of its maximum possible speed, and the camera is in a circular equatorial orbit with a circumference six times the circumference of the horizon. See a video of this model on this book's page at Interstellar.withgoogle.com.

There are two very special stars in Gargantua's sky with the gravitational lens turned off. One lies just above Gargantua's north pole, the other just below its south pole. These are analogues of the North Star, which is located exactly above the north pole of the Earth. I have placed five-pointed stars on the primary (red) and secondary (yellow) images of Gargantua's pole stars. All the stars in Earth's sky seem to revolve around Polaris as we are being pulled around by the Earth's rotation. Similarly, in Gargantua, all primary star images revolve around the red images of the pole stars as the camera moves around the hole, but their reversal trajectories (for example, two red turbulence curves) are strongly distorted by the spatial vortex and the gravitational lens. Similarly, all secondary star images revolve around the yellow polar star images (eg, along two distorted yellow curves).

Why, in the case of a non-rotating black hole (Figure 8.4), was it seen that the secondary images emerge from the black hole's shadow, rotate around the hole, and descend back into the shadow, rather than revolve around in a closed curve, as in Gargantua's case (Figure 8.5)? Actually, they are apply along a closed curve in the case of a non-rotating black hole. However, the inner edge of this closed curve is so close to the edge of the shadow that it cannot be seen. Gargantua's rotation creates a spatial vortex, and this vortex pushes the inner Einstein ring outward, revealing the pattern of complete reversal of the secondary images (yellow curves in Figure 8.5) and the inner Einstein ring.

Inside the inner Einstein ring, the jet pattern is more intricate. The stars in this region are tertiary and even higher-order images of all the stars in the universe - the same ones seen as primary images outside of the outer Einstein ring and as secondary images between the Einstein rings.

In Figure 8.6, I show five small pictures of Gargantua's equatorial plane, with Gargantua itself in black, the camera's orbit in pink dotted lines, and the beam of light in red. The beam of light carries the image of a star to the camera, which is located at the tip of the blue arrow. The camera moves around Gargantua counterclockwise.

You can really get into the gravitational lens if you walk through these pictures one by one on your own. Note that the true direction to the star is up and to the right (look at the outer ends of the red rays). The camera and the beginning of each beam points to the image of the star. The tenth image is very near the left edge of the shadow, and the right secondary image is near the right edge; comparing the camera directions for these images, we can see that the shadow spans an arc of about 150 degrees in the upward direction. This is despite the fact that the actual direction from the camera to the center of Gargantua is to the left and up. The lens shifted the shadow relative to Gargantua's present position.

Rice. 8.6. Rays of light that carry images of stars at the tips of the blue arrows. (English primary - primary, secondary - secondary, tertiary - tertiary.) [From the same Double Negative model as in figures 8.1 and 8.5.]

Creating Black Hole and Wormhole Visual Effects in Interstellar

Chris wanted Gargantua to look like in fact looks like a rapidly spinning black hole up close, so he asked Paul to consult me. Paul put me in touch with the team Interstellar, which he assembled at Double Negative's visual effects studio in London.

I got into a frenzy working closely with Oliver James, the chief scientist. Oliver and I talked on the phone and Skype, exchanged emails and files, and met in person in Los Angeles and at his office in London. Oliver has degrees in optics and atomic physics and understands Einstein's laws of relativity, so we spoke the same technical language.

Some of my fellow physicists have already made computer models of what an observer would see while orbiting a black hole, or even falling into one. The best judges were Alain Riazuelo from the Institut d'Astrophysique in Paris and Andrew Hamilton at the University of Colorado at Boulder. Andrew created a video about black holes that is shown in planetariums around the world, and Alain has modeled black holes that spin very, very fast, like Gargantua.

So my original intention was to set Oliver up with Alain and Andrew and ask them to provide him with the required input. For several days I was uncomfortable with this decision, and then I changed my mind.

During my half-century career as a physicist, I made great efforts, making new discoveries myself and educating students who made new discoveries. Why not, for a change, do something just because it's fun, I asked myself, even if others have done it before me? So I lashed out at that "something". And it was fun. And to my surprise, as a by-product it led (modestly) to new discoveries.

Using the laws of relativity and drawing heavily on the work of predecessors (notably Brandon Carter at Laboratoire Univers et Théories in France and Jeanne Levine at Columbia University), I deduced the equations Oliver needed. These equations calculate the paths of light rays starting from some source of light, such as a distant star, and moving through Gargantua's curved space towards the camera. From these rays of light, my equations then calculate the images seen by the camera, taking into account not only the light sources and Gargantua's space and time distortion, but also the movement of the camera around the Gargantua.

Once I got these equations, I tried them out myself with a friendly software called Mathematica. I compared the images generated by my Mathematica computer code with those of Alain Riazuelo, and when they agreed, I rejoiced. I then wrote detailed descriptions of my equations and sent them to Oliver in London, along with my Mathematica code.

My code was very slow and low resolution. Oliver's task was to translate my equations into computer code that could produce the ultra-high quality IMAX images needed for the film.

Oliver and I did it step by step. We started with a non-rotating black hole and a stationary camera. Then we added the rotation of the black hole. Then we added camera movement: first moving in a circular orbit, and then falling into a black hole. And then we switched to a camera revolving around a wormhole.

At this point, Oliver hit me like a bolt from the blue: in order to model the most subtle effects, he would need not only equations describing the paths of light rays, but also equations describing how the cross section of a beam of light changes size and shape, passing through a wormhole .

I more or less knew how to do it, but the equations were terribly confusing and I was afraid of making mistakes. So I searched the technical literature, and found that in 1977 Serge Pineault and Rob Rouber of the University of Toronto got the necessary equations in almost the form I needed. After three weeks of wrestling with my own stupidity, I reshaped their equations in exactly the right form, expressed them in Mathematica, and painted them for Oliver, who incorporated them into his own computer code. After all, his code was able to produce the quality images needed for the film.

In Double Negative, Oliver's computer code was just the beginning. He handed it to the art team led by Eugenie von Tanzelmann, who added an accretion disk () and created a background galaxy with stars and nebulae that would be distorted by the Gargantua lens. Her team then added Endurance, Rangers and landers and camera animations (changing movement, direction, field of view, etc.) and molded the images into very convincing forms: into incredible scenes that appear in the film. Continued, see.

In the meantime, I've been racking my brains over the high-quality videos Oliver and Evgenia have sent me, trying hard to figure out why the images look the way they do, and the starfields flow the way they do. For me, these videos are like experimental data: they reveal things that I would never have figured out on my own, without these models - for example, what I described in the previous section (Figures 8.5 and 8.6). We are going to publish a technical article or two describing what we have learned.

Appearance of Gravity Slings

Although Chris chose not to show any of the gravity slings in Interstellar, I wondered what they would have looked like to Cooper as he led the Ranger to Miller's planet. So I used my equations and Mathematica to model the images. (My images have a much lower resolution than Oliver and Eugenia's due to the slowness of my code.)

Figure 8.7 shows a series of images seen from Ranger Cooper as it pumps around an Intermediate Mass Black Hole (IBH) to begin its descent towards Miller's planet - my scientific interpretation. Interstellar. This is the sling described in figure 7.2.

Figure 8.7. Gravity sling around the CHDSM with Gargantua in the background [My own model and rendering.]

In the top image, Gargantua is at the back with the HRSM passing in front of her. The CHDSM captures rays of light from distant stars directed towards Gargantua, scrolls them around itself and throws them towards the camera. This explains the donut of starlight surrounding the shadow of the CHDSM. Although the HRSM is a thousand times smaller than Gargantua, it is much closer to Ranger than Gargantua, so it looks only moderately smaller.

As the PRSM moves to the right for the sling-moving camera, it leaves behind the primary shadow of Gargantua (the middle picture in Figure 8.7), and pushes the secondary image of Gargantua's shadow in front of it. These two images are completely analogous to the primary and secondary images of a star refracted by the gravitational lens of a black hole; but now the PDSM lens refracts Gargantua's shadow. In the bottom image, the size of the secondary shadow is shrinking as the PDSM moves further. At this point, the gravity sling is nearly complete, and the camera aboard the Ranger zooms down to Miller's planet.

Impressive as these images are, they can only be seen close to the CHDSM and Gargantua, and not from a great distance to the Earth. For terrestrial astronomers, the most impressive optical effects of giant black holes are the jets protruding from them and the light from the sparkling disk of gas in their orbit. We will now turn to them.

In the film, the radius of the wormhole is 1 kilometer, the length of the trough is 10 meters, and the lensing radius is 50 meters larger than the hole.

The wormhole is unstable and really wants to close and turn into two black holes.

The longer the wormhole, the more smeared copies of objects behind the hole will be visible in it, because the light has more ways to enter the eye (at different angles, you can enter the hole and exit at one point).

To keep a wormhole open, you need a lot of exotic negative mass stuff to push everything on the opposite side out of the hole. Such a substance, theoretically, can exist, but it is unrealistic to find it in sufficient quantity to hold a hole.

But there is a second option for holding wormholes: you need to use the gravitational forces from the fifth dimension. If a four-dimensional object pierces our three-dimensional space, it creates very strange forces in it that are not like anything else. Here they are to be used to hold the wormhole.

Gargantua outside

That's enough mass to keep the tidal forces on Miller's planet from tearing it in half.

Endurance is parked at a distance of 10 AU, and orbits at c/3 (100,000 km/s), in the opposite direction of Gargantua's rotation.

Hole image:

• Gargantua is flattened to the left because it rotates from left to right (relative to the camera) and light traveling in the direction of rotation has a better chance of not being sucked into the event horizon.
• Every star behind a black hole has two images in the picture: the regular one, which is far from the hole, is given by light that is slightly bent by gravity. And second, inside the Einstein sphere, such a sphere that refracts everything very strongly, because it is close to the hole. There are a few more features associated with the rotation of the hole, but I can hardly explain it, because optics are not my best side.

To prevent the accretion disk from frying everyone alive with all possible rays, it was made with a temperature of only a couple of thousand degrees, like the Sun, it emits light and quite a bit of gamma and X-rays. It is precisely because of the weakness of the disk that plasma beams do not erupt from the south and north poles from Gargantua, as from a quasar. This is possible if the hole did not "eat" other planets for a long time.

What glows in the pictures is the accretion gas disk.
And it looks like hell, understand that, because, thanks to gravitational lensing, above and below a black hole, a piece of a disk is visible behind this very hole.

Very close to Gargantua's event horizon, there are two critical orbits formed by the balance of gravity and centrifugal force.
On one of them the planet Manna moves, on the other - Endurance at the end of the film.

five-dimensional space

If the fifth (as well as the sixth, seventh, etc.) dimensions exist, then they must be folded into a tube or compressed very quickly, otherwise gravity from our three dimensions will propagate according to laws other than 1/r^2.

Space in Interstellar consists of three three-dimensional branes in four-dimensional anti-de Sitter space. There are bounding branes above and below our brane, they are needed so that hyperspace is curved between layers and human laws of the distribution of forces, in particular gravity, are not violated. So, in general, you can make the fifth dimension unfolded, and not twisted into a tube.

Hyperspace curves between these branes and the distance measured in the top or bottom brane will be very much shorter than in our brane. The distance between these branes should be 1.5 centimeters - this is enough for the distance along the top brane between the Earth and Gargantua to be 1AE, and our brane obeyed Newton's laws of gravity.

To land on the planet Miller, which rotates at a speed of 0.55 s, you need to do two gravitational maneuvers: first, stop the rotation of the Ranger completely so that the hole attracts the ship, and in front of the planet Miller, slow down another c / 4 speed and land.

How to do it? it not shown in film, but Kip suggests that at least two more small black holes, the size of the Earth, must be orbiting Gargantua. Only by falling into the gravity of such holes, you can slow down so much and not kill the crew of the ship. At the same time, in the film, Cooper says that he needs to make a maneuver around a neural star, and not a black hole (I honestly do not remember this phrase).

The waves on the planet Miller are caused by the planet's "wobble" back and forth, about an axis perpendicular to Gargantua. Like a tsunami.

Miller's planet must lie between the accretion disk and Gargantua. But Nolan decided not to shoot the ending, and put the planet you know how. The planet is heated from the accretion disk.

Mann's planet is in a very squiggly orbit at c/20 .

To reach Manna's planet, Cooper had to perform two gravitational maneuvers: around a small black hole orbiting Gargantua, then fly up to Manna's planet at a speed of c/2, and after making a couple of orbits around it, reduce the speed to c/20

The clouds on Manna's planet are made of "dry ice" carbon dioxide. On the surface - ordinary ice. When the planet Manna flies closer to Gargantua and its disk, carbon dioxide evaporates - clouds are obtained.

Flying towards a black hole

How did Cooper pick up a falling Endurance? Pulled him high enough for Gargantua's pull to pull him and Cooper into critical orbit. Don't forget that when Endurance crashes into Mann's planet, the planet is very close to Gargantua.

The critical orbit in which Cooper navigates the ship around Gargantua is the field in which centrifugal force, which pushes the ship out of orbit, and the force of gravity, which pulls the ship into the hole, are the same. In this orbit, you can forever revolve around Gargantua, but with one condition: you cannot move a single step from orbit, since the ship will either be thrown away from Gargantua, or it will fall into a black hole. This orbit is unstable. It is worth saying that the orbit of the planet Miller is exactly the same, but stable, it is difficult to get off it.