The Science of Interstellar

In Interstellar, as the Ranger approaches Miller’s planet carrying Cooper and his crew, we see Gargantua in the sky above, 10 degrees across (twenty times larger than the Moon as seen from Earth!) and surrounded by its bright accretion disk. See Figure 17.9. As startlingly impressive as this may be, Gargantua’s angular size has actually been reduced greatly from what it would really be at the location of Miller’s planet.

If Miller’s planet is, indeed, close enough to Gargantua to experience extreme time slowing—as I chose for my interpretation of the movie—then it must be deep into the cylindrical region of Gargantua’s warped space, as depicted in Figure 17.1. It seems likely, then, that if you look down the cylinder from Miller’s planet you will see Gargantua, and if you look up the cylinder you will see the external universe; so Gargantua should encompass roughly half of the sky (180 degrees) around the planet and the universe the other half. Indeed, that is what Einstein’s relativistic laws predict.

It also seems clear that, since Miller’s planet is the closest anything can live stably, without falling into Gargantua, the entire accretion disk should be outside the orbit of Miller’s planet. Therefore, as the crew approach the planet, they should see a giant disk above them and a giant black-hole shadow below. Again, that is what Einstein’s laws predict.

If Chris had followed these dictates of Einstein’s laws, it would have spoiled his movie. To see such fantastic sights so early in the movie would make the movie’s climax, when Cooper falls into Gargantua, visually anticlimactic. So Chris consciously saved such sights for the end of the movie; and invoking artistic license, near Miller’s planet he depicted Gargantua and its disk together, “just” twenty times bigger than the Moon looks from Earth.

^{Fig. 17.9. Gargantua and its disk, partially eclipsed by Miller’s planet, as the Ranger, in the foreground, descends toward landing. [From Interstellar, used courtesy of Warner Bros. Entertainment Inc.]}

Although I’m a scientist and aspire to science accuracy in science fiction, I can’t blame Chris at all. I would have done the same, had I been making the decision. And you’d have thanked me for it.

18 Gargantua’s Vibrations

While Cooper and Amelia Brand are on Miller’s planet, Romilly stays behind in the Endurance, observing Gargantua. From exquisitely accurate observations, he hopes to learn more about gravitational anomalies. Above all (I presume), he hopes that quantum data from Gargantua’s singularity (Chapter 26) will leak out through the event horizon, bringing information about how to control the gravitational anomalies (Chapter 24). Or, in Romilly’s pithy language, bringing information for “solving gravity.”

When Amelia Brand returns from Miller’s planet, Romilly tells her, “I learned what I could from studying the black hole, but I couldn’t send anything to your father. We’ve been receiving but nothing gets out.”

What did Romilly observe? He’s not specific, but I presume he would focus on Gargantua’s vibrations, and I offer this chapter’s extrapolation of the movie for that.

Vibrations of Black Holes

In 1971 Bill Press, a student of mine at Caltech, discovered that black holes can vibrate at special, resonant frequencies, in much the same way as a violin string vibrates.

When a violin string is plucked just right, it emits a very pure tone: sound waves with a single frequency. When plucked a little differently, it emits that pure tone and also higher harmonics of the pure tone. In other words (if the string is firmly clamped, with the clamping finger not moving around) its vibrations produce sound at only a discrete set of frequencies, the string’s resonant frequencies.

The same is true of a wine glass whose rim you rub with your finger, and a bell struck by a hammer. And also a black hole disturbed by something falling into it, Press discovered.

A year later Saul Teukolsky, another of my students, used Einstein’s relativistic laws to work out a mathematical description of these resonant vibrations for a spinning black hole. (That’s the best thing about teaching at Caltech; we get fabulous students!) By solving Teukolsky’s equations, we physicists can compute a black hole’s resonant frequencies. But solving them for an extremely fast spinning hole (like Gargantua) is very difficult. So difficult that it was not done successfully until forty years later—by a collaboration in which the lead players again were two Caltech students: Huan Yang and Aaron Zimmerman.