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 and 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 to 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 inner most 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 and 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 inner most 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 so 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 Rison 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 and 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 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 back side 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 happen 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 and 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 and 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?