It’s Professor Dave, I wanna tell you how
to make a black hole.
We just learned about what happens to very
high-mass stars when they die.
Once one of these runs out of fuel in its
core, left with lots of iron and little else
to fuse, there is nothing preventing gravitational
collapse any longer.
The outer layers plummet inwards in a single
second, overcoming electron degeneracy pressure,
and even neutron degeneracy pressure, generating
a shock wave that triggers a supernova, and
leaves behind a black hole.
A single point containing most of the mass
of the star.
As much as this sounds like science fiction,
we have mountains of direct evidence for these
objects, even within our galaxy, so let’s
learn some more about these things and what
they do.
First of all, why are black holes black?
To answer this, let’s highlight some basics
regarding escape velocity.
As we may remember, general relativity tells
us that massive objects warp spacetime, and
the greater the mass, the more pronounced
the influence.
This is why objects fall down from the sky
to the ground, they are simply following the
curvature of space that is produced by the
mass of the very nearby earth.
But something can escape earth’s gravitational
pull if it can travel away from the earth
at a velocity that exceeds the earth’s escape velocity.
This means it is traveling so fast that it
can climb out of the curvature, kind of like
a ball rolling fast enough to get all the
way up a hill.
We can calculate the escape velocity for a
massive object by using this equation, where
G is the gravitational constant, M is the
mass of the object, and R is the radius of
the object.
For earth, that ends up being about 11.2 kilometers
per second.
It’s pretty tough to get going this fast,
but we’ve managed to do it with every shuttle
and probe that has made it into space.
But let’s notice that radius is in the denominator.
That means that if you contain the same mass
in a smaller region, the escape velocity gets larger.
This is because the increasing density of
the object will result in a more profound
curvature of space.
In the limit of a massive object with zero
radius, the escape velocity becomes infinite,
meaning that no object can escape the gravity
of a black hole, no matter how fast it travels,
even light, which travels at the speed of
light, the fastest anything can go, as we
learned when we talked about special relativity
in the modern physics course.
If light can’t leave an object to reach
our eyes, then we can’t see it, and that’s
why black holes are black.
This brings us to an interesting conclusion.
Anything that is sufficiently dense so as
to have an escape velocity greater than the
speed of light must therefore be a black hole.
Taking our previous equation and plugging
in c for V, and then solving for R, we can
plug in any mass we want into this equation
and solve for the radius within which that
object must be compressed in order to generate
a black hole.
This is called the Schwarzschild radius of
an object.
When a high-mass star collapses at the end
of its life, it is compressed well beyond
its Schwarzschild radius, which is the most
common way that the universe produces a black hole.
But hypothetically, anything could become
a black hole if sufficiently compressed.
Of course, the amount of compression required
is staggering.
For the earth to become a black hole, it would
need to have a radius of just under a centimeter.
That’s all the mass of the entire world
contained within something less than the size
of a gumball.
Even a person like you or me could become
a black hole, but we would have to be compressed
into a sphere with a radius of ten to the
negative 25 meters, which is as much smaller
than an atom as an atom is smaller than a person.
So it’s not such an easy task, which is
why we don’t see black holes in our day-to-day lives.
So we know that all the material in a black
hole is contained within its Schwarzschild
radius, and there is a related term for describing
this radius, which is called the event horizon.
This is the region of spacetime surrounding
the black hole within which light can’t
escape, and for a non-rotating black hole,
the distance to the event horizon is equal
to the Schwarzchild radius.
We can consider this the boundary of the black
hole in a certain sense, not because it’s
the edge of the matter producing the black
hole, but rather because beyond this edge,
spacetime is sufficiently warped such that
light can’t leave it and get to our eyes.
But if we can’t see black holes, how do
we know they exist?
Well there are many ways to observe black
holes indirectly.
Sometimes one star in a binary system becomes
a black hole, and material from the other
star begins accreting around what appears
to be absolutely nothing.
This activity emits X-rays that we can receive,
which helps us identify that a black hole
is there.
More recently, we have been able to detect
gravitational waves emitted from a pair of
black holes that are merging.
Sometimes we can even see large collections
of stars moving very fast around a region
of seemingly empty space.
By measuring their velocities we can calculate
the mass of what they must be orbiting, and
it will typically be many solar masses, and
that’s a black hole too.
Sometimes it will have a mass equal to many
millions of solar masses, and we call this
a supermassive black hole.
These can form over billions of years if black
holes swallow up enough material from their
surroundings, or even merge with other black
holes, and we have very convincing evidence
that suggests there is a supermassive black
hole at the center of every large galaxy in
the universe, including ours.
So what can possibly stop black holes from
swallowing up everything in the universe?
Well, for one thing, space is huge.
Objects very close to a black hole may be
doomed, but if you get far enough away from
one, its gravity is no different than if it
was a regular object.
In other words, if our sun became a black
hole today, we would certainly be in trouble
in the sense that we wouldn’t receive any
more light and heat, but surprisingly, earth’s
orbit wouldn’t change at all.
The black hole would still have the same mass
as the sun, so orbits would remain unperturbed.
Another interesting feature of black holes
was predicted by physicist Stephen Hawking.
Against all intuition, it was found that black
holes actually emit radiation, which we refer
to as Hawking radiation.
This can be understood by recalling the Heisenberg
Uncertainty Principle, which allows for particle-antiparticle
pairs to appear out of the quantum foam.
One possible explanation claims that when
such a quantum fluctuation occurs right at
the event horizon of a black hole, one of
these particles will fall into the black hole
while the other escapes, and for energy conservation,
the one that fell in will be the one with
negative energy.
This ever so slightly reduces the mass of
the black hole.
This process is perpetual but painfully slow,
with a solar-mass black hole requiring around
ten to the 67 years to completely evaporate.
But, it does mean that even black holes eventually
die, just like everything else in the universe.
So with that, beyond having learned how to
make black holes and supermassive black holes,
we now know enough about stars to start learning
about the types of stars that have existed
throughout the lifetime of the universe so
far, and the structures that they have come
together to form, so let’s check that out next.
