The Science of Interstellar

^{Fig. 5.3. Signals I send after crossing the event horizon can’t get out. Note: Because one space dimension is removed from this diagram, I am a two-dimensional Kip, sliding down the warped two-dimensional surface, part of our brane. [My own hand sketch.]}

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] and since the future inside the hole is downward, away from the horizon, nothing can escape back upward, through the horizon.

Space Whirl

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.

^{Fig. 5.4. Space around a spinnning black hole is dragged into whirling motion. [My own hand sketch.]}

Precise Depiction of the Warped Space and Time Around a Black Hole

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.

^{Fig. 5.5. Precise depiction of the warped space and time around a rapidly spinning black hole: one that spins at 99.8 percent of the maximum possible rate. [Drawing by Don Davis based on a sketch by me.]}

In the fully accurate Figure 5.5, I don’t depict the hole’s interior. We’ll get to that later, in Chapters 26 and 28.

The warping in Figure 5.5 is the essence of a black hole. From its details, expressed mathematically, physicists can deduce everything about the black hole, except the nature of the singularity at its center. For the singularity, they need the ill-understood laws of quantum gravity (Chapters 26).

A Black Hole’s Appearance from Inside Our Universe