The Science of Interstellar

But there was a problem with this choice. At this distance, Gargantua would look huge; it would subtend about 50 degrees on the Endurance’s sky. Truly awe inspiring, but undesirable for so early in the movie! So Chris and Paul chose to make Gargantua look much smaller at the parking orbit: about two and a half degrees, which is five times the size of the Moon as seen from Earth—still impressive but not overwhelmingly so.

The Shell of Fire

Gravity is so strong near Gargantua, and space and time are so warped, that light (photons) can be trapped in orbits outside the horizon, traveling around and around the hole many times before escaping. These trapped orbits are unstable in the sense that the photons always escape from them, eventually. (By contrast, photons caught inside the horizon can never get out.)

I like to call this temporarily trapped light the “shell of fire.” This fire shell plays an important role in the computer simulations (Chapter 8) that underlie Gargantua’s visual appearance in Interstellar.

For a nonspinning black hole, the shell of fire is a sphere, one with circumference 1.5 times larger than the horizon’s circumference. The trapped light travels around and around this sphere on great circles (like the lines of constant longitude on the Earth); and some of it leaks into the black hole, while the rest leaks outward, away from the hole.

When a black hole is spun up, its shell of fire expands outward and inward, so it occupies a finite volume rather than just the surface of a sphere. For Gargantua, with its huge spin, the shell of fire in the equatorial plane extends from the bottom red circle of Figure 6.3 to the upper red circle. The shell of fire has expanded to encompass Miller’s planet and the critical orbit, and much, much more! The bottom red circle is a light ray (a photon orbit) that moves around and around Gargantua in the same direction as Gargantua spins (the forward direction). The upper red circle is a photon orbit that moves in the opposite direction to Gargantua’s spin (the backward direction). Evidently, the whirl of space enables the forward light to be much closer to the horizon without falling in than the backward light. What a huge effect the space whirl has!

The region of space occupied by the shell of fire above and below the equatorial plane is depicted in Figure 6.4. It is a large, annular region. I omit the warping of space from this picture; it would get in the way of showing the shell of fire’s full three dimensions.

^{Fig. 6.4. The annular region around Gargantua, occupied by the shell of fire.}

Figure 6.5 shows some examples of photon orbits (light rays) trapped, temporarily, in the shell of fire.

The black hole is at the center of each of these orbits. The leftmost orbit winds around and around the equatorial region of a small sphere, traveling always forward, in the same direction as Gargantua’s spin. It is nearly the same as the bottom (inner) red orbit in Figures 6.3 and 6.4. The next orbit in Figure 6.5 winds around a slightly larger sphere, in a nearly polar and slightly forward direction. The third orbit is larger still, but backward and nearly polar. The fourth is very nearly equatorial and backward, that is, nearly the upper (outer) red equatorial orbit of Figures 6.3 and 6.4. These orbits are actually inside each other; I pulled them apart so they are easier to see.

Some photons that are temporarily trapped in the shell of fire escape outward; they spiral away from Gargantua. The rest escape spiraling inward; they spiral toward Gargantua and plunge through its horizon. The nearly trapped but escaping photons have a big impact on Gargantua’s visual appearance in Interstellar. They mark the edge of Gargantua’s shadow as seen by the Endurance’s crew, and they produce a thin bright line along the shadow’s edge: a “ring of fire” (Chapter 8).

^{Fig. 6.5. Examples of light rays (photon orbits) temporarily trapped in the shell of fire, as computed using Einstein’s relativistic equations.}

7 Gravitational Slingshots

Navigating a spacecraft near Gargantua is hard because the speeds are very high. To survive, a planet or star or spacecraft must counteract Gargantua’s huge gravity with a comparably huge centrifugal force. This means it must move at very high speed. Near the speed of light, it turns out. In my science interpretation of Interstellar, the Endurance, parked at ten Gargantua radii while the crew visit Miller’s planet, moves at one-third the speed of light: c/3, where c represents the speed of light. Miller’s planet moves at 55 percent the speed of light, 0.55c.