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