The Science of Interstellar

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

The star images outside the Einstein ring (the primary images, let’s call them) move in the way one might expect: smoothy from left to right, but deflecting away from the black hole as they move. (Can you figure out why the deflection is away from the hole instead of toward it?)

^{Fig. 8.4. The changing star pattern seen by the camera as it moves rightward in its orbit in Figure 8.3. [From the simulation by Alain Riazuelo; see www2.iap.fr/users/riazuelo/interstellar.]}

However the secondary images, inside the Einstein ring, move in an unexpected manner: They appear to emerge from the right edge of the shadow, move outward into the annulus between the shadow and the Einstein ring, swing leftward around the shadow, and descend back toward the shadow’s edge.

You can understand this by going back to the upper drawing in Figure 8.3. The right ray passes near the black hole, so the right stellar image is near its shadow. Earlier in time, when the camera was further leftward, the right ray had to pass even closer to the black hole in order to bend more strongly and reach the camera, so the right image was very close to the edge of the shadow. By contrast, earlier in time, the left ray passed rather far from the hole and so was nearly straight and produced an image rather far from the hole.

Now, if you’re ready, think through the subsequent motions of the images, depicted in Figure 8.4.

Lensing by a Rapidly Spinning Black Hole: Gargantua

The whirl of space generated by Gargantua’s very fast spin changes the gravitational lensing. The star patterns in Figure 8.1 (Gargantua) look somewhat different from those in Figure 8.4 (a nonspinning black hole), and the streaming patterns differ even more.

For Gargantua the streaming (Figure 8.5) reveals two Einstein rings, shown as pink curves. Outside the outer ring, the stars stream rightward (for example, along the two red curves), as they did for a nonspinning black hole in Figure 8.4. However, the whirl of space has concentrated the stream into narrowed high-speed strips along the back edge of the hole’s shadow, strips that bend somewhat sharply at the equator. The whirl has also produced eddies in the streaming (the closed red curves).

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

^{Fig. 8.5. The star streaming patterns as seen by a camera near a rapidly spinning black hole such as Gargantua. In this simulation by the Double Negative visual-effects team, the hole spins at 99.9 percent of the fastest possible, and the camera is in a circular, equatorial orbit with circumference six times larger than the horizon’s circumference. For a film clip of this simulation, see this book’s page at Interstellar.withgoogle.com.}

There are two very special stars in Gargantua’s sky with gravitational lensing turned off. One lies directly above Gargantua’s north pole; the other directly below its south pole. These are analogs of the star Polaris, which resides directly above the Earth’s north pole. I placed five-pointed stars at the primary (red) and secondary (yellow) images of Gargantua’s pole stars. All the stars on the Earth’s sky appear to circulate around Polaris as we humans are carried around by the Earth’s rotation. Similarly, all of Gargantua’s primary stellar images circulate around the red pole-star images as the camera orbits the hole, but their circulation paths (for example, the two red eddy curves) are highly distorted by the whirl of space and gravitational lensing. Similarly, all the secondary stellar images circulate around the yellow pole-star images (for example, along the two distorted yellow curves).