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 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 Star,
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 into 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 radiu
now, in all likelihood
the blackhole 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 in to the singularity,
or spiral out and head off to infinity.
Now the question I want to answer is
what does this black quote-on-quote 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 ray.
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 horizon,
it too will get bend
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 radius 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.
We 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.
但其实 其中某一点 会弥漫在阴影上
It gets weirder than that.
Because the light can come in and go around the back
and they 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 telescope.
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 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 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.
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 for last week.
I guess what will be exciting
is to watch it over time how it changes, right?
There’s a lot of hope that there are blobs moving around.
If you see a blob going round the front
and then it goes around the back
then you see it in the back image etc.
And that’s gonna be kind of cool.
On Wednesday April 10th 2019