### Mary Mary, quite contrary, how does your black hole grow?

One of the most distant black holes we’ve yet observed: the quasar 3c186. [Credit: NASA/CXC/SAO/A.Siemiginowska et al. Optical: AURA/Gemini Obs.]

Shameless self-promotional opening: In less than two weeks, I’m teaching an online class on black holes, so you can consider this post as an extended advertisement. Sign up today (afternoon and evening sections!), and please spread the word!

All the real black holes we’ve discovered so far are surrounded by matter. In fact, that’s how we’ve found them: as matter orbits, falls into, or is ejected by the black hole, it emits a lot of light, turning a technically invisible object into something exceedingly bright. However, that same brightness prevents us (so far!) from probing close to the region that defines a black hole: its event horizon.

The event horizon is the black hole’s boundary: once anything crosses the horizon, it can’t return to the outside Universe. If you were unlucky enough to fall in, you wouldn’t hit a surface or see anything special happening at that boundary,[1] you just would never be able to reverse your course. Even turning your ship around and firing your engines at full throttle would make you reach the black hole’s center that much faster![2]

The death plunge of an object near a black hole. Click the image for more information on what these plots represent.

Imagine if we could observe a black hole from a distance without all that matter surrounding it, allowing us to do a kind of controlled experiment by dropping particles into it. Specifically, let’s send a small probe with nothing aboard but a flashing beacon of green light, timed to blink once every second. The beacon will appear green and blink at one-second intervals for most of its journey, but as it gets close to the black hole, the flashes will begin to change.

Gradually, the green light will turn yellow, orange, red, then into infrared, microwave, and ultimately radio light as its wavelength is stretched by gravity. The flashes will also slow down, with more time passing between blinks. Eventually the flashes will be so weak and far apart that the probe will be lost to us.

But we’ll never see the probe cross the event horizon. Technically from the equations of general relativity, we’ll measure time coming to a halt for the probe when it reaches the horizon, freezing everything at that moment. Practically, the moment the signal fades — which will happen in a finite time — the probe is lost to us, but we still can’t see it entering the black hole.

That begs the question: how can a black hole ever increase in mass?

### It’s what’s outside that counts

The structure of a rotating black hole, somewhat simplified. All the mass is concentrated into a ring at the center. As with the non-rotating case, there’s a boundary called the event horizon; inside that boundary, an object would need to move faster than light to escape. The ergosphere is a region within which nothing can stay at rest, which I’ll discuss in detail below. The photon sphere will be discussed in part 3 of this series. [Credit: moi]

Too start to answer that question, we need to switch perspectives. Namely, if you and I decided to be foolish and take a spaceship into the black hole instead of sending a probe, we’d see something very different. The journey across the event horizon wouldn’t take forever from our point of view: it would be over momentarily, and the rest of the trip to the center of the black hole would similarly take very little time. And of course once we reached that center, that’s the end of time.[3]

I’m not (just) being melodramatic. The different perspectives — falling into the black hole vs. observing an object falling in from a distance — have already demonstrated that time is measured relative to the observer. If our foolhardy spaceship was equipped with a green beacon flashing once per second like the probe, our friends back on Earth would see the flashes behave the same way as in the previous description. They would also see us living forever, though not in such a way to enjoy it. (See Gateway and its sequels by Frederick Pohl for a science-fiction treatment of the topic.)

From the perspective of an observer on Earth, our passage to the center of the black hole will always take place in the future, no matter how long they wait. By extension, whatever lies at the very heart of a black hole isn’t anything you can observe in the lifetime of the Universe. That’s true whether it’s an infinite concentration of mass as predicted by general relativity, or whatever replaces that in a quantum theory of gravity. However, that’s not to say it’s not important: black holes can grow over time as matter falls in, whether we can observe it directly or not.[4]

That’s because gravity is due to all the mass (and energy content, thanks to $E = mc^2$) within a region. Any matter that gets “stuck” to the event horizon from our point of view contributes to the total gravitational influence of the black hole to any object outside the horizon. Thus, when a black hole eats a star, the gas is added to the total mass of the black hole even if we never see it fall in. So, while it’s unlikely we “see” the mass of the singularity or whatever at the center of the black hole, we see something more meaningful: that mass plus whatever else the black hole gathers to itself over time. In a real sense, the immediate future of the black hole is what determines where the event horizon is: matter “stuck” to it will be part of the black hole in the future, but we see the effects of it now.

This isn’t an abstraction, either. Various processes in the central regions of galaxies depend on this kind of crazy physics. Work by Roger Penrose, Stephen Hawking, and others showed that black holes will inevitably form when massive stars collapse on themselves. Not only that, the spin of a black hole governs the way matter falls in or gets ejected back into space.

That the mass doesn’t enter the horizon is just our opinion: we aren’t in possession of all the facts. While there’s no real consistent way to think of anything from the black hole’s point of view, we do know particles do pass through the event horizon from their frame of reference — and the gravitational field of the black hole reflects that.

### Notes

1. I’m only talking about black holes as described by general relativity, but theories including quantum phenomena may point to different behaviors. One such idea is the black hole firewall: intense radiation produced at the event horizon that would destroy anything passing through. That’s a topic of intense debate, which I wrote about for Slate; see also these explanations from Jennifer Ouellette and Zeeya Merali.
2. I guess I can’t leave that one alone, can I? According to general relativity, motion under gravity alone maximizes the amount of time that passes in your frame of reference. If you accelerate, you cut down on the amount of time along your trajectory, so once you’re inside the event horizon, firing your rockets will take you to your inevitable fate that much more quickly.
3. Whether we can survive the tidal forces near the event horizon is another matter. For a small black hole, like Cygnus X-1, the answer is probably no: we’d fall victim to spaghettification, wherein the strength of the forces on the side of the spaceship closer to the horizon would be enough stronger than those on the far side to tear the ship — and us — to bits. For a supermassive black hole, we’d likely be OK, or at least as OK as anyone can be if they’re falling into a black hole.
4. Another way black holes can grow is by merging, but that’s another topic for another day. For a taste, see my earlier piece in Nautilus.