If light doesn’t have rest mass, why can’t it escape a black hole?
Because nothing escapes a black hole.
Then how does gravity escape a black hole?
It doesn’t.
What about Hawking radiation?
Nothing escapes a black hole!!
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Hey Crazies.
There are a lot of misconceptions about black holes out there.
Let’s see if we can fix a few.
We’ll start with the one I hear the most:
The escape velocity at the event horizon is the speed of light.
Wrong!
That gives you the impression that, if you could somehow travel faster than light,
you could escape a black hole, which simply isn’t true.
What’s escape velocity?
A concept entirely in the realm of classical physics.
Say you’ve got a squirrel you want to launch into space.
With one momentary burst of acceleration, what upward speed is required for it to escape
Earth’s gravitational pull?
That’s the escape velocity.
Emphasis on the word "momentary."
A rocket doesn’t work like this.
A rocket has continuous thrust, which isn’t what we’re talking about.
Instead we mean BOOM!
Suddenly the squirrel is going really fast.
Fast Fast!
After that, it’s only affected by gravity.
We’re even ignoring the surrounding air.
Physics Land!! Ah!!
I keep forgetting about that.
Anyway, how fast does this thing need to go to escape?
Well, considering the energy transformation, it comes out to be this.
G is a constant.
These two are the mass and radius of the Earth or wherever you’re launching from.
Mars.
The Moon.
Whatever.
It seems pretty natural to take a concept like this to the extreme.
There should be some choice of R such that the resulting speed is the speed of light.
Except this would be wrong.
It’s wrong because we wouldn’t be considering relativity.
While Newton’s laws apply to 99% of the things in 99% of the universe,
black holes and the speed of light are distinctly not those things.
They’re in the other 1% of 1%.
When you take physics to its extremes, you have to use extreme models.
The friendly simple ones just don’t work anymore.
We need to use general relativity, which says gravity isn’t actually pull anything.
No, there isn’t an invisible hand reaching out and grabbing things.
No, there isn’t any transmission of information telling things what to do.
No, space itself is not falling inward.
According to general relativity, gravity is the curvature of space-time.
Gravity is geometry.
You might be picturing something like this.
Stop that right now.
Space isn’t two-dimensional.
It’s three-dimensional, so it looks more like this.
Although that still ignores time, which we really shouldn’t do.
The space-time geometry around any non-rotating spherical object
is described by something called the Schwarzschild metric.
OMG! I actually said it right that time!
This tells us how far apart nearby events are in time and space.
You can see that depends on how close you are to the source of curvature.
Is it OK for that R to be in the denominator like that?
Nope. No, it isn't.
When denominators go to zero in a model, we call that a singularity
and, if you’re paying attention, there are actually two of them in here.
If all the mass is compressed into a single point,
we get what’s called a physical singularity at R=0.
But there’s also this negative exponent, which means this term flips over
and we run into another problem at the Schwarzschild radius,
otherwise known as the radius of the event horizon.
Yes, the event horizon is a second singularity for the black hole.
We called it a coordinate singularity
because you can remove it with a change in coordinates.
Bottom line though, a distant observer sees a problem at the event horizon,
but someone falling into the black hole does not.
I did a whole video about this a while back.
Wait, isn’t that Schwarzschild radius the same as?
No! No. It only looks the same.
Just let me explain.
Here’s what we got earlier for an escape velocity at the speed of light
and here's the Schwarzschild radius.
Yes, they look the same, but that’s just a coincidence.
While those results are the same, they were derived using completely different models,
which means they mean different things.
An event horizon has nothing to do with escape velocity.
An event horizon is about causality.
It’s about time.
What happens as something falls into a black hole is difficult to understand,
at least until we add a time axis.
The squirrel’s path through space-time would normally be straight upward through time.
This region represents all possible futures the squirrel could have,
the edges of which are the paths taken by light signals it might send.
But because of the black hole, the squirrel’s actual future is curved.
As it falls in, more and more of its future points toward the black hole.
It isn’t being pulled in.
It just goes in because that’s where the future goes.
This is taken to the extreme at the event horizon.
Before the squirrel crosses the horizon, there are still some possible futures
that would allow it to escape.
It would just have to accelerate really hard.
Once it crosses though, all of its possible futures point inward.
Even if it tries to send signals, those will also go inward, no matter the direction.
It’s a trap!!
Once you’re inside, there’s no such thing as outward.
It’s like that house from Warehouse 13 where, if you try to leave,
you’re just still in the house.
So, how does the gravity get out?
It doesn’t.
Have you even been listening?
Gravity is just what we call it when space and time are curved.
It doesn’t have to escape because that geometry is already on the outside.
You’re only trapped if you end up inside the event horizon
and the reason you’re trapped is because all your possible futures point inward.
It’s not that you can’t escape.
It’s simply that you won’t escape.
Black holes don’t capture objects.
They don’t capture light.
Black holes capture the future.
Whoa Dude.
So was this clear enough for everyone?
Let us know in the comments.
Thanks for liking and sharing this video.
Don’t forget to subscribe if you’d like to keep up with us.
And until next time, remember, it’s OK to be a little crazy.
The most common question from the last video was:
What is momentum-space?
It’s just a visual way to represent the random quantum motions of the neutrons
inside the neutron star.
Don’t overthink it.
Anyway, thanks for watching!