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? 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