Escape From a Black Hole

The black hole: the inner boundary of the known universe, the point of no return. This is the region in the vicinity of a gravitational singularity which, once entered, cannot be left.
Or can it?

Black holes are mysterious, almost arcane objects, but this particular property—their inescapability—arises naturally as a consequence of Einstein’s theory of general relativity. Every massive body has an escape velocity, the “launch speed” you’d need to get free of its gravitational pull and avoid falling back down to its surface. This depends on the mass of the body, but also its radius, your distance from its center of mass. On earth, the escape velocity is something like 11.2 km/s, but if you imagine a much denser earth—the same mass as our planet, but smaller—it would be correspondingly harder to escape. Conversely, if you started out a few kilometers above earth’s surface, the escape velocity would be much lower.

The event horizon is the spherical, imaginary surface around a stationary black hole where the escape velocity reaches c, the speed of light. Get any closer than this distance, called the Schwarzschild* radius, and even a photon traveling directly away from the singularity will not move fast enough to escape its gravitational pull.

While it may seem at first like the phrases “event horizon” and “Schwarzschild radius” could be used interchangeably, this is only the case for an uncharged, non-rotating black hole. But since virtually all astronomical objects have some spin angular momentum, there’s no reason to assume that a typical black hole would be stationary.

Spinning a black hole modifies some of its properties in a very interesting way: suddenly, the event horizon is no longer at the Schwarzschild radius. Instead, it shrinks down, up to half its original size, depending on the black hole’s rotational velocity. In the space between this new event horizon and the original Schwarzschild radius is a region known as the ergosphere.

Image Credit: Wikipedia user MesserWoland, CC BY-SA

The ergosphere is a fascinating structure, where everything—down to the fabric of spacetime itself—is dragged along, forced to co-rotate with the black hole. Outside the ergosphere, this effect is noticeable, but not inevitable: if we flew fast enough counter-spinward, we could stay in one place with respect to a distant observer.  At the surface of the ergosphere, however, we would need to fly at c in order to maintain this position, which is impossible. A photon located precisely at the edge of the ergosphere’s equator, traveling against the direction of the black hole’s rotation, would find itself trapped—moving as fast as possible with respect to the spacetime around it, but totally stationary with respect to the distant stars.

Seen from above the plane of spin, the ergosphere looks like a disc. A photon, red, is trapped at the surface of the ergosphere, moving at c but totally stationary to an outside observer.

This same frame-dragging effect is what makes it possible to escape from the vicinity of a rotating black hole, at a distance where a non-rotating one would be guaranteed to suck you in.

A photon moving at c, which hits the ergosphere’s surface moving counter-spinward, will be trapped in place. If it’s any closer to the center than the outer surface, it will attempt to move counter-spinward, but will appear to move spinward from the perspective of an outside observer. Mathematically, this photon’s energy is negative from our perspective, which is a very surprising result; a massive particle in a similar situation would seem to have negative mass.

However, if a particle—say, a spacecraft—is orbiting spinward, traveling with the rotation direction of the black hole, it will experience a “speed boost” from a distant observer’s frame as it approaches the black hole. If the spacecraft has enough fuel and fires its engines in the right way, it can return from the ergosphere, substantially accelerated by the black hole’s frame-dragging effects in a supercharged version of the “gravitational slingshot” effect. The black hole, meanwhile, will actually have its rotation slowed: the inertia of the ship, as well as the fuel it left behind, saps spin from the central object as it brings them up to speed.

Although black holes are almost always described as inescapable, this thought experiment is not a new one; it dates back to 1971, when Roger Penrose published his paper “Extraction of Rotational Energy From a Black Hole”, earning this technique the name of the “Penrose Process”. While it’s obviously never been utilized by humans, and I’m highly doubtful that it ever will, the Penrose process may be responsible for some of the high-energy X-ray emissions we see coming from distant galaxies’ cores, so it’s a potentially useful tool for helping astronomers understand the dynamics of things like quasars and pulsars.

More than that, though, the black hole and its ergosphere are great places to stretch your imagination. It’s a frontier that we’re still coming to understand, and such frontiers are always rich in discovery. When the black hole loses some angular momentum to accelerate our spacecraft, the ergosphere shrinks; does that mean that the photon that was trapped at the surface is suddenly freed? What happens when two ergospheres interact, and spacetime is pulled in two different directions at once? We can’t be certain of the answers to these questions right now, but when we find out, they’re sure to be exciting.

*Karl Schwarzschild was the first one to mathematically describe the “point of no return” that defines what we typically think of as a black hole. The fact that his last name is German for “black shield” is an absolutely maddening coincidence.

You may also read these articles