Kip Thorne - The Science of Interstellar

The black hole Gargantua plays a major role in Interstellar . Let’s look at the basic facts about black holes in this chapter and then focus on Gargantua in the next.

First, a weird claim: Black holes are made from warped space and warped time. Nothing else—no matter whatsoever.

Now some explanation.

Imagine you’re an ant and you live on a child’s trampoline—a sheet of rubber stretched between tall poles. A heavy rock bends the rubber downward, as shown in Figure 5.1. You’re a blind ant, so you can’t see the poles or the rock or the bent rubber sheet. But you’re a smart ant. The rubber sheet is your entire universe, and you suspect it’s warped. To determine its shape, you walk around a circle in the upper region measuring its circumference, and then walk through the center from one side of the circle to the other, measuring its diameter. If your universe were flat, then the circumference would be π = 3.14159… times the diameter. But the circumference, you discover, is far smaller than the diameter. Your universe, you conclude, is highly warped!

Space around a nonspinning black hole has the same warping as the trampoline: Take an equatorial slice through the black hole. This is a two-dimensional surface. As seen from the bulk, this surface is warped in the same manner as the trampoline. Figure 5.2 is the same as Figure 5.1, with the ant and poles removed and the rock replaced by a singularity at the black hole’s center.

The singularity is a tiny region where the surface forms a point and thus is “infinitely warped,” and where, it turns out, tidal gravitational forces are infinitely strong, so matter as we know it gets stretched and squeezed out of existence. In chapters 26, 28, and 29, we see that Gargantua’s singularity is somewhat different from this one, and why.

For the trampoline, the warping of space is produced by the rock’s weight. Similarly, one might suspect, the black hole’s space warp is produced by the singularity at its center. Not so. In fact, the hole’s space is warped by the enormous energy of its warping. Yes, that’s what I meant to say. If this seems a bit circular to you, well, it is, but it has deep meaning.

Just as it requires a lot of energy to bend a stiff bow in preparation for shooting an arrow, so it requires a lot of energy to bend space; to warp it. And just as the bending energy is stored in the bent bow (until the string is released and feeds the bow’s energy into the arrow), so the warping energy is stored in the black hole’s warped space. And for a black hole, that energy of warping is so great that it generates the warping.

Warping begets warping in a nonlinear, self-bootstrapping manner. This is a fundamental feature of Einstein’s relativistic laws, and so different from everyday experience. It’s somewhat like a hypothetical science-fiction character who goes backward in time and gives birth to herself.

This warping-begets-warping scenario does not happen in our solar system hardly at all. Throughout our solar system the space warps are so weak that their energy is minuscule, far too small to produce much bootstrapped warping. Almost all the space warping in our solar system is produced directly by matter—the Sun’s matter, the Earth’s matter, the matter of the other planets—by contrast with a black hole where the warping is fully responsible for the warping.

When you first hear mention of a black hole, you probably think of its trapping power as depicted in Figure 5.3, not its warped space.

If I fall into a black hole carrying a microwave transmitter, then once I pass through the hole’s event horizon , I’m pulled inexorably on downward, into the hole’s singularity. And any signals I try to transmit in any manner whatsoever get pulled down with me. Nobody above the horizon can ever see the signals I send after I cross the horizon. My signals and I are trapped inside the black hole. (See Chapter 28 for how this plays out in Interstellar .)

This trapping is actually caused by the hole’s time warp. If I hover above the black hole, supporting myself by the blast of a rocket engine, then the closer I am to the horizon, the more slowly my time flows. At the horizon itself, time slows to a halt and, therefore, according to Einstein’s law of time warps, I must experience an infinitely strong gravitational pull.

What happens inside the event horizon? Time is so extremely warped there that it flows in a direction you would have thought was spatial: it flows downward toward the singularity. That downward flow, in fact, is why nothing can escape from a black hole. Everything is drawn inexorably toward the future, [12] If it is possible to go backward in time, you can only do so by traveling outward in space and then returning to your starting point before you left. You cannot go backward in time at some fixed location, while watching others go forward in time there. More on this in Chapter 30. and since the future inside the hole is downward, away from the horizon, nothing can escape back upward, through the horizon.

Black holes can spin, just as the Earth spins. A spinning hole drags space around it into a vortex-type, whirling motion (Figure 5.4). Like the air in a tornado, space whirls fastest near the hole’s center, and the whirl slows as one moves outward, away from the hole. Anything that falls toward the hole’s horizon gets dragged, by the whirl of space, into a whirling motion around and around the hole, like a straw caught and dragged by a tornado’s wind. Near the horizon there is no way whatsoever to protect oneself against this whirling drag.

These three aspects of spacetime warping—the warp of space, the slowing and distortion of time, and the whirl of space—are all described by mathematical formulas. These formulas have been deduced from Einstein’s relativistic laws, and their precise predictions are depicted quantitatively in Figure 5.5 (by contrast with Figures 5.1–5.4, which were only qualitative).

The warped shape of the surface in Figure 5.5 is precisely what we would see from the bulk, when looking at the hole’s equatorial plane. The colors depict the slowing of time as measured by someone who hovers at a fixed height above the horizon. At the transition from blue to green, time flows 20 percent as fast as it flows far from the hole. At the transition from yellow to red, time is slowed to 10 percent of its normal rate far away. And at the black circle, the bottom of the surface, time slows to a halt. This is the event horizon. It is a circle, not a sphere, because we are looking only at the equatorial plane, only at two dimensions of our universe (of our brane). If we were to restore the third space dimension, the horizon would become a flattened sphere: a spheroid. The white arrows depict the rate at which space whirls around the black hole. The whirl is fast at the horizon, and decreases as we climb upward in a spacecraft.