In the 1987 movie, Spaceballs,
which is a parody of the Star Wars franchise,
a mysterious force called the Schwartz allows Dark Helmet to battle Lone Star.
Upon engaging in battle,
Dark Helmet says to Lone Star,
"I see that your Schwartz is as big as mine."
Strictly speaking, the Schwartz has nothing to do with black holes.
But this scene is an easy way to remember
the Schwarzschild radius is a measurement of the size of a black hole.
In order to size up a black hole,
you need to be able to deduce how massive it is.
The first major tool for discovering
the properties of black holes was developed by Einstein,
who first published his field equation formalism for general relativity in 1915.
Einstein himself wasn't confident that his equations allowed exact solutions.
I mean, just look at this mess.
Well, luckily there are some people out there that don't listen to Einstein.
Amazingly, a solution to Einstein's equations was developed by a German astronomer
named Karl Schwarzschild the same year that Einstein introduced general relativity.
Schwarzschild's solution to Einstein's field equations
give us the first glimpse at the nature of black holes.
The result, of course,
is the expression for the Schwarzschild radius.
This equation relates the mass of a black hole with the size of its event horizon.
The best part, Karl's solution to Einstein's equations were exact,
making Einstein extremely happy.
At first, it wasn't recognized that the Schwarzschild solution described black holes.
In those early days, they called them totally gravitationally collapsed objects.
Only much later, in 1957,
were they formally called black holes.
Schwarzschild provided a convenient equation for deducing
the radius of a black hole knowing only its mass.
But, that still leaves us with a problem.
We can't travel to a black hole to measure the size of its event horizon.
So, how are we supposed to deduce the mass of a black hole, in the first place?
Karl Schwarzschild was serving in the German army when he
wrote the solution in a letter to Einstein in December, 1915.
Unfortunately, Schwarzschild was suffering from
a skin condition and succumbed to it only six months later.
He died on May 11th,
1916 without knowing the impact his work would have in the era of modern physics.
Why then is it so hard to measure the properties of black holes?
Think about it like this, humans have five senses that we can use to touch,
taste, smell, see, and hear objects in our environment. We're really good at it.
We can distinguish millions of colors,
thousands of smells, hundreds of tastes, etc.
There's a reason for the English idiom,
"A picture is worth a thousand words."
But, black holes have none of these things.
They can't be tasted,
smelled, they have no color,
they make no sound.
But above all, they emit no light.
Back in 1967, an astrophysicist named Werner Israel,
a professor here at the University of Alberta,
was the first to demonstrate why black holes were so elusive.
He showed that if any large feature existed on the black hole surface,
like mountains or hair,
they would tend to smooth out.
Scientists now call this the "no-hair theorem".
The name is used to illustrate that black holes have
no other independent characteristics than their mass, charge, and spin.
There are no black holes with ponytails, mullets or mohawks,
because if indeed they had any kind of identifying feature on their event horizon,
well, it would get sucked into the black hole.
A black hole's event horizon is a featureless boundary,
just like the scene in Spaceballs where
Dark Helmet is searching the desert on the moon of Vega.
If you try to comb a black hole,
you aren't going to find anything.
When you rub a balloon against your head,
you create a difference in charges between your head and the balloon.
Your hair, charged with static electricity,
will stand up straight while the balloon can now stick to a nearby wall.
A law of physics, called the law of conservation of charge,
tells us that charge can't be created or destroyed.
So, even when charges are separated,
they're always balanced between positive and negative charges.
Since black holes don't have hair,
you can't rub a balloon against them.
But, a black hole can have charge.
This might happen if say,
a statically charged balloon is carried across the event horizon,
but not the head of hair with the balancing charge.
However, there is a force of
electrostatic attraction between the positive and the negative which like gravity,
will pull these two objects together.
This means that any charged black hole will
attract the opposite charge and eventually, it will become neutral.
Most black holes are theorized to be neutrally charged.
The opposite is true for black hole spin.
We mostly talk about black holes that have no spin.
But, what would happen if say,
I throw a frisbee that is rotating in?
Any of the angular momentum carried by the frisbee will have to
be transferred to the black hole once it crosses the event horizon.
A Schwarzschild black hole is a non spinning black hole,
and these types of black holes aren't very realistic.
Out in space, even a spinning frisbee is enough to impart spin on a black hole.
We've spent an awful lot of this lesson telling you
what you can't measure about black holes.
So now we need to ask what you can measure.
Well, a black hole all by itself isn't going to tell you everything you want to know.
A second object is required,
something that's big enough and even bright enough for us to
see which will interact with the black hole and therefore reveal its secrets.
I'm leaving you in good hands,
but before I go,
may the Schwarzschild be with you.
