- Hello and welcome to a black hole coding challenge.

Time has really slowed down for me,

or maybe it's sped up.

I can't remember which is which because

I'm actually now recording this many days

after the actual livestreamed coding challenge.

In a little bit, I will change my clothes and

travel into the past through the black hole.

I don't know how it's all going to work,

but you will see me live coding,

writing the code to do this simulation.

In truth, it's less simulation than visualization.

On April 10th,

the first ever image of a black hole was published.

This image was put together by a team of scientists

known at the Event Horizon Telescope.

It was compiled from data from many telescopes

all over the Earth all synchronized.

I looked at this image and I thought,

it looks kind of fuzzy and glowy and

maybe there's some way I could reproduce

this image through a simulation.

I started to sort of dig into this.

I quickly realized I'm many, many steps away from doing that

and I wanted to find the place to start,

somewhere where I could at least begin to

simulate or visualize the behavior of

space time and black holes.

Here are the resources that I used to learn about this.

First, let me thank Veritasium's video,

the how to understand the image of a black hole.

This video was actually published

the day before the image was revealed,

which is really kind of amazing.

If you watch this video, the explanation is superb.

In particular, there's a short animation in the video

that depicted beams of light traveling

towards the black hole,

some disappearing into the black hole,

some wrapping around in an orbit.

That's my starting point where I was interested in.

I also learned quite a bit from Chris Orbin

and the STEM Coding YouTube channel.

STEM Coding, if you're not familiar

with that YouTube channel,

you should definitely check it out.

They have a lot of videos about physics and science

taught through the lens of coding and visualization.

In particular, they have a video called

Slingshot with Gravity and Chris Orbun

published an article explaining how that

code example could be tweaked a little bit

to kind of get at some of the ideas

around how gravity and black holes.

Finally, there's a wonderful paper from 1978.

Thank you to Veritasium also for this reference

called Image of a Spherical Black Hole

with Thin Accretion Disk.

This paper has diagrams and the mathematics

behind the photon trajectories around a black hole.

It gives you a lot of background into

what you would want to do to visualize a black hole.

Of course, I'm not the first one to try this.

Many people have made beautiful visualizations

and artistic renderings of black holes.

There's the one that you might remember

from the move Interstellar.

Kip Thorn, a Caltech physicist,

was actually an advisor on that film,

but there's a lot of artistic license there.

I also want to point out to you Ricardo Antonelli

who's written this wonderful article

How to Draw a Black Hole,

Geodesic Raytracing in Curved Space Time.

In the article he goes through step-by-step

a bunch of different computer graphic tricks and techniques

along with the sort of physics of black holes themselves

to create a 3D visual of what a black hole might look like.

If you've watched me before,

you know I am not a physicist, I'm not a scientist.

There are many caveats.

I don't play a physicist on YouTube.

I'm just here wanting to make something

in 2D Canvas JavaScript.

In fact, I already did it.

What I'm here right now,

let me talk to you about the pieces

that I want to put in this visualization

as a sort of reference point for when I start coding.

The black hole that I want to visualize is in the galaxy M87.

It previously didn't have a name.

It was just called M87 star, the star for black hole,

but it was recently named Powehi.

I'm not sure if I'm pronouncing that correctly,

but it is from a Hawaiian chant

and it means something like adorn, dark,

fathomless creation, something like that.

Very appropriate for a black hole.

This is what's known as a super massive black hole.

Not all black holes are super massive,

but this one is and its mass is equivalent to

2.6 billion solar masses, or suns.

Take the sun, our sun,

the one up in the sky that shines on us,

and put together 2.6 billion of those

and you have a black hole.

It's so massive, we can't see it.

Why?

Because the gravitational pull is so strong,

there's so much matter in there,

that any light traveling towards it,

once it gets to a certain proximity, can no longer escape.

You couldn't be inside the black hole

and shine a flashlight.

You could be there, but outside the black hole,

you couldn't see it 'cause the light can't get out.

Of course, you couldn't also be there because

you would be dead, very, very dead in the black hole,

or you'd just be like Matthew McConaughey,

one or the other is true.

This little ring here,

this distance from the center of black hole

at which nothing can escape, not even light,

not even the fastest thing we know about light can escape,

is known as the event horizon.

There's actually a formula for calculating

the distance from the center of black hole

to that event horizon itself,

the Schwarzschild radius, or R sub S.

The Schwarzschild radius is calculated as two times G,

the universal gravitational constant, times M,

the mass of the black hole itself,

remember, 2.6 billion solar masses,

divided by C squared where C is the speed of light.

Of course, the event horizon isn't really a circle.

It's a sphere, but for us in our 2D simulation,

we're going to make it flat.

In order to actually calculate this,

I need some of these values.

I have the mass, I also need C, the speed of light,

which I'm looking over there, I don't have this memorized,

which is 299,792,458 meters per seconds squared.

That's very, very fast.

Not seconds squared.

I don't know why I put seconds squared there.

It's just meters per second.

This number, meters per second.

That's the speed of light.

I also need G, the universal gravitational constant,

which is 6.67 times 10 to the negative 11th power.

Now, with these values, with the mass of the black hole,

with the universal gravitational constant,

with the speed of light, you can actually calculate this.

I will leave that to you to calculate

and leave your answer in the comments,

or you could probably looks it up

because people are calculating this stuff all the time.

Another element that I want to include

in my visualization is the accretion disk.

The accretion disk is a whole lot of matter

that's outside of the event horizon

orbiting the black hole and sort of feeding the black hole.

This is a particularly active one.

Again, a black hole isn't emptiness.

It's we think of it as emptiness.

There's just so much matter there

that the light cannot escape so it's nothingness.

So crazy.

The accretion disk is this orbit that's

outside of matter orbiting.

It has a specific measurement where it is,

which is three times the Schwarzschild radius.

From the center, one, two, three.

You can see not drawn to scale,

but this is the accretion disk, three RS.

What about light?

The accretion disk is full of matter.

Matter has mass and it's orbiting at some speed

and we could calculate gravitational attraction

and all that stuff,

but light travels at the speed of light,

photons of light travel the speed of light, that speed,

and have the mass of zero.

It so happens that at 1.5, right around here,

at 1.5 times the Schwarzschild radius,

this is where light will orbit, but not in a stable orbit.

Any photons, any light that's orbiting there

will eventually either spiral out forever or spiral in

pass the event horizon,

never to be seen or heard from again.

These are the elements I want in my visualization.

I want to depict the black hole right here,

really the shadow of the black hole,

measured with the event horizon.

I want this photon ring,

but both the event horizon is really a sphere

and this photon ring is really a photon sphere,

this is the place where light is orbiting,

it's not a stable orbit.

It doesn't slow down so it's always

eventually going to shoot out or shoot in, but ultimately,

if you were standing there,

the light would actually draw a circle

and you would see the back of your head,

which is not what's happening to me right now

and I'm trying to think of that.

My mind doesn't work that way.

I want to depict that and then the accretion disk as well.

These are the elements that I want in my visualization.

However, I want to animate something.

I want to look at what happens when

light itself is traveling at the black hole.

What does it do?

We could be pretty sure that if I

take a beam of light, a photon,

and point it directly at the center of the black hole,

it's going to travel up to the black hole,

go past the event horizon, and never come back.

We're never going to hear from it again.

It sucked into the event horizon.

What happens if though there's a beam of light over here,

or over here, or over here?

What happens there?

We can actually see a diagram of this

in Ricardo Antonelli's tutorial.

This is really the core inspiration for

what it is that I want to create in p5.js.

What you see here is basically my visualization.

There's the black hole, there's the photon ring,

here are beams of light, they're bending around,

they sort of temporarily end up in that orbit,

and then spiral out or spiral in.

The thing is, are they really bending,

going in a curved path,

or are they simply traveling in a

straight line through the curve of space time?

This is where it would be useful to talk about relativity.

The theory of relativity will help to explain

why the space time bends around an object,

a super massive object.

You can think of it as space time being this trampoline

and there's a big bowling ball sitting in the center

and it's just weighing it down and the

space time around it starts to bend

and things start to fall in towards it.

That's ultimately what's happening with a black hole.

The theory of relativity is beyond the scope

of what I'm doing in this video.

I just want to look at is there a way

that I can create the effect.

What if I take these beams of light, photons,