How to Understand What Black Holes Look Like

On Wednesday, April 10th, 2019, you will probably see the first-ever image of a black hole. That's when the Event Horizon Telescope will be releasing their results, and I haven't seen them yet, but I think they're going to look something like this. I can be relatively confident because, well, it's gonna look a bit like a fuzzy coffee mug stain. But if you are disappointed by this image, I think that misses the gravity of the situation.

From this image, we should be able to tell whether the general theory of relativity accurately predicts what happens in the strong gravity regime; that is, what happens around a black hole. What I want to do here is understand what exactly we are seeing in this image, so here is my mock black hole of science, and this sphere represents the event horizon. That is the location from which not even light fired radially away from the black hole could be detected by an outside observer.

All of the world lines end up in the center of the black hole, in the singularity. Once you're inside here, there is no coming back, not even for light. The radius of the event horizon is known as the Schwarzschild radius. Now, if we were just to look at a black hole with nothing around it, we would not be able to make an image like this because, well, it would just absorb all electromagnetic radiation that falls on it. But the black hole that they're looking at, specifically the one in the center of our Milky Way galaxy, Sagittarius A*, has matter around it in an accretion disk.

In this accretion disk, there is dust and gas swirling around here very chaotically. It's incredibly hot; we're talking millions of degrees, and it's going really fast—a significant fraction of the speed of light. And it's this matter that the black hole feeds off and gets bigger and bigger over time. But you'll notice that the accretion disk does not extend all the way in to the event horizon. Why is that? Well, that's because there is an innermost stable circular orbit, and for matter around a non-spinning black hole, that orbit is at three Schwarzschild radii.

Now, in all likelihood, the black hole at the center of our galaxy will be spinning, but for simplicity, I'm just considering the non-spinning case. You can see my video on spinning black holes if you want to find out more about that. So, this is the innermost orbit for matter going around the black hole. If it goes inside this orbit, it very quickly goes into the center of the black hole, and we never hear from it again. But there is something that can orbit closer to the black hole, and that is light.

Because light has no mass, it can actually orbit at 1.5 Schwarzschild radii. Now, here I'm representing it with a ring, but really this could be in any orientation, so it's a sphere of photon orbits. If you were standing there, of course, you could never go there, but if you could, you could look forward and actually see the back of your head because the photons could go around and complete that orbit. Now, the photon sphere is an unstable orbit, meaning eventually either the photons have to spiral into the singularity or spiral out and head off to infinity.

Now, the question I want to answer is: What does this black "quote-unquote" shadow in the image correspond to in this picture of what's actually going on around the black hole? Is it the event horizon? Are we simply looking at this? Or is it the photon sphere, or the innermost stable circular orbit? Well, things are complicated, and the reason is this black hole warps space-time around it, which changes the path of light rays, so they don't just go in straight lines like we normally imagine that they do.

I mean, they are going in straight lines, but space-time is curved, so yeah, they go in curves. The best way to think of this is maybe to imagine parallel light rays coming in from the observer and striking this geometry here. Of course, if the parallel light rays cross the event horizon, we'll never see them again, so they're gone. That will definitely be a dark region, but if a light ray comes in just above the event horizon, it too will get bent and end up crossing the event horizon; it ends up in the black hole.

Even a light ray coming in the same distance away as the photon sphere will end up getting warped into the black hole and curving across the event horizon. So in order for you to get a parallel ray which does not end up in the black hole, you actually have to go out 2.6 radii away. If a light ray comes in 2.6 Schwarzschild radii away, it will just graze the photon sphere at its closest approach and then it will go off to infinity.

So the resulting shadow that we get looks like this: It is 2.6 times bigger than the event horizon. You say, "What are we really looking at here? What is this shadow?" Well, in the center of it is the event horizon. It maps pretty cleanly onto the center of this shadow, but if you think about it, light rays going above or below also end up crossing the event horizon just on the backside.

So, in fact, what we get is the whole backside of the event horizon mapped onto a ring on this shadow. So, looking from our one point in space at the black hole, we actually get to see the entirety of the black hole's event horizon. I mean, maybe it's silly to talk about seeing it because it's completely black, but that really is where the points would map to on this shadow.

It gets weirder than that because the light can come in and go around the back and say get absorbed in the front. You get another image of the entire horizon next to that, and another annular ring, and then another one after that, and another one after that, and you get basically infinite images of the event horizon as you approach the edge of this shadow.

So what is the first light that we can see? It is those light rays that come in at just such an angle that they graze the photon sphere and then end up at our telescopes. And they produce a shadow which is 2.6 times the size of the event horizon. So this is roughly what we'd see if we happened to be looking perpendicular to the accretion disk, but more likely we will be looking at some sort of random angle to the accretion disk.

We may be even looking edge-on. And in that case, do we see this shadow of the black hole? You might think that we wouldn't, but the truth is, because of the way the black hole warps space-time and bends light rays, we actually see the back of the accretion disk. The way it works is light rays coming off the accretion disk bend over the top and end up coming to our telescopes, so what we end up seeing is something that looks like that.

Similarly, light from the bottom of the accretion disk comes underneath, gets bent underneath the black hole, and comes towards us like that. This is where we get an image that looks something like the interstellar black hole. It gets even crazier than this because light that comes off the top of the accretion disk here can go around the back of the black hole, graze the photon sphere, and come at the bottom right here, producing a very thin ring underneath the shadow.

Similarly, light from underneath the accretion disk in the front can go underneath and around the back and come out over the top, which is why we see this ring of light here. This is what we could see if we were very close to the black hole—something that looks truly spectacular.

One other really important effect to consider is that the matter in this accretion disk is going very fast, close to the speed of light. So if it's coming towards us, it's gonna look much brighter than if it's going away. That's called relativistic beaming or Doppler beaming, and so one side of this accretion disk is going to look much brighter than the other, and that's why we're gonna see a bright spot in our image.

So hopefully, this gives you an idea of what we're really looking at when we look at an image of a black hole. If you have any questions about any of this, please leave them in the comments below, and I will likely be making a video for the launch of the first-ever image of a black hole, so I'll try to answer them then. Until then, I hope you get as much enjoyment out of this as I have because this has truly been my obsession for like the last week.

I guess what would be exciting is to watch it over time, how it changes, right? There's a lot of hope that there are blobs moving around, and you know, if you see a blob going round the front and then it goes around the back, but you see it in the back image, etc., then that's gonna be kind of cool.