In this lecture we'll talk about black holes,
what it would be like to visit a black hole,
and how astronomers locate black holes.
White dwarfs and neutron stars are strange
enough, but things can get even weirder when
it comes to black holes.
Let's go back to where we left off with the
death of a massive star.
We had a neutron star held up by neutron degeneracy
pressure.
If the mass of the neutron star exceeds three
solar masses, neutron degeneracy pressure
can no longer support the star against gravity.
The neutron star will collapse turning into
a black hole.
The idea of a black hole was predicted in
the late 1800s, and to understand where the
idea came from, we need to think again about
escape velocity.
An object of a certain mass has an escape
velocity.
This is the velocity you need to escape the
object's gravity.
On Earth, for example, you need to be moving
at about 12 kilometers per second to break
free of Earth's gravity.
Remember, the force of gravity decreases with
distance according to the inverse-square law.
This means if we move farther way from the
Earth's center of mass, gravity will be less,
and the escape velocity- the velocity we need
to break free of gravity- decreases.
We need even less velocity needed if we launch
from a taller tower!
Now imagine what would happen if we could
shrink Earth, keeping its mass the same.
The smaller we make Earth, the closer the
surface is to the center of mass.
Therefore gravity on the surface increases
and we'd need a larger escape velocity to
break free.
If you continue to shrink Earth, at some point,
the escape velocity will get very large.
It will approach the speed of light, and when
it does, nothing- not even light- can escape.
If you shrink Earth down to about the size
of a peanut, light would not be able to escape
the surface, and Earth would become a black
hole.
By definition a black hole is an object whose
gravity is so powerful that not even light
can escape.
To talk about the size of a black hole, we
need to introduce the Schwarzschild Radius.
This is the radius at which the escape velocity
reaches the speed of light.
In equation form it's equal to 2 times the
gravitational constant, G, times the mass
of the object, divided by the speed of light
squared.
G and c are both constants.
Therefore the Schwarzschild radius depends
only on the mass of the object.
The boundary between the inside of a black
hole and the universe outside is called the
event horizon.
It is the boundary around the black hole at
which the escape velocity equals the speed
of light.
Nothing that passes within this boundary can
ever escape.
The event horizon gets its name from the fact
that we have no hope of learning anything
about events that occur within it.
We usually think of the size of a black hole
as the radius of the event horizon.
However it's not really possible to measure
radius of a black hole because its center
lies within the event horizon and it's not
part of our universe.
We therefore define the radius of the black
hole as the radius it would have it geometry
were flat.
The radius of the event horizon is known the
Schwarzschild radius that we defined earlier.
The structure of space and time near the event
horizon is very strange.
Einstein taught us that space and time are
woven together into a four-dimensional spacetime.
The general theory of relativity tells us
that what we perceive as gravity actually
arises from the curvature of spacetime.
It's nearly impossible to visualize four dimensions
at once, but we can get the basic idea with
a two dimensional analogy.
Imagine a rubber sheet to represent two-dimensional
slices through spacetime.
In this analogy, the sheet is flat when it's
far away from anything with mass.
The sheet will become more curved near a massive
object.
Mass warps the fabric of spacetime.
The more massive the object more, the more
spacetime gets warped.
The curvature of spacetime near a black hole
is so great that the rubber sheet forms a
bottomless pit.
A collapsing stellar core becomes a black
hole at the moment it shrinks to a size smaller
than its Schwarzschild radius.
The black hole still contains all the mass,
but its outward appearance tells us nothing
about what fell in.
We have no way of answering the question of
what lies inside a black hole.
No information can ever emerge from within
the event horizon.
Because nothing can stop the crush of gravity
in a black hole, all the matter that forms
a black hole should be crushed to an infinitely
tiny and dense point in the black hole's center
called a singularity.
This isn't going to happen, but theoretically,
what do you think would happen if our Sun
became a black hole?
Do you think we would we get sucked in?
Happily, no.
The only way to get sucked in is to cross
the event horizon.
The Sun has a Schwarzschild radius of about
3 kilometers.
Therefore, if the Sun became a black hole
we'd have to get within 3 kilometers in order
to cross the event horizon.
The orbits of the planets would not change,
although without the light from the Sun, I
doubt life on Earth would make it.
Maybe the roaches would survive.
I don't know.
It's interesting to think about what would
happen if we were to visit a black hole.
So let's take an imaginary journey to a 10
solar mass black hole with a Schwarzschild
radius of 30 kilometers.
We can then do some experiments to test general
relativity.
Einstein's theory of general relativity says
that time should run more slowly as the force
of gravity grows stronger.
It also predicts that light coming out of
a strong gravitational field will be redshifted.
To see how the gravity of a black hole affects
time, we'll take two synchronized clocks from
our spaceship and send one toward the event
horizon of the black hole on a small shuttle.
We'll see that something strange happens to
the clock that is traveling toward the black
hole.
If we watch the clock as it moves toward the
black hole, we find that it runs more slowly
than our ship clock.
Also, it turns red.
Eventually it's redshifted so much, that we
can't see it at all.
You may think the clock we sent to the event
horizon had some sort of defect.
Let's say you want to do your own experiment.
You take another synchronized clock and head
out to the event horizon yourself, and those
of us on the ship put one of our clocks up
to the window so you can see it as you move
toward the event horizon.
As you get closer to the black hole, you would
notice a couple of things.
First, your clock appears to be working normally.
It's not slowing down or turning red for you.
Second, if you look at the ship's clock, it's
turning blue and moving faster!
As you continue to approach the black hole,
the force of gravity grows very strong.
It will pull much harder on your feet than
your head, and stretch you into a spaghetti
noodle.
Sadly, you could not survive falling into
a black hole.
From the perspective of those of us on the
ship, we would never actually see you cross
the event horizon.
From our point of view, you'll be redshifted
so much that you vanish.
Even if we could see you, from our perspective,
your time comes to a stop.
So you would appear to hover for all eternity
on the edge of the event horizon.
What we are observing near the black hole
are the effects of general relativity.
The clock near the black hole appears to slow
down because of time dilation.
The clock appears to turn red because of a
gravitational redshift.
This is a redshift due to gravity rather than
to the Doppler effect.
Black holes may seem so strange that it makes
sense to wonder if they really exist.
And if they do, how would we find one?
We can't observe black holes directly.
But we can infer the presence of a black hole
if it is part of a binary system.
If we see a star orbiting something that we
can't see, we can work out the possible mass
of the objects using Newton's generalization
of Kepler's laws.
If the mass of the unseen companion exceeds
the 3 solar-mass neutron star limit, it's
possible we have ourselves a black hole.
Observational evidence for black holes formed
by supernovae comes from studies of X-ray
binaries.
We learned earlier that the accretion disks
around neutron stars in close binary systems
can emit strong X-ray radiation, making an
X-ray binary.
Because a black hole has even stronger gravity
than a neutron star, a black hole in a close
binary system should also be surrounded by
a hot, X-ray emitting accretion disk.
Some X-ray binaries may therefore contain
black holes rather than neutron stars.
One famous X-ray binary with a likely black
hole is in the constellation Cygnus.
And here is a table listing some likely black
hole candidates.
And that's all for black holes.
I hope it wasn't too crazy.
Take care, get yourself a coffee, I will talk
to you soon.
