 We've been talking a bit
about black holes lately
and we'll continue to do so.
We tend to be pretty theoretical
in how we think of them, partly
because the theory
predicts some fun stuff
that no human will
likely ever experience.
In fact, the second
part of this episode
will be the answer to our Escape
the Kugelblitz Challenge, which
is highly theoretical and in
fact, a little implausible.
So to ground us a
little bit first,
I want to talk about
actual real black holes,
in particular, how
we see these things.
There's been no reasonable
doubt about the reality
of black holes for some time.
Although they don't emit
any light themselves,
they can have a very visible
effect on their surroundings.
The most spectacular effect
is when black holes feed.
Matter falling into the
extreme gravitational well
of a black hole will
reach incredible speeds
and temperatures, causing
the region around black holes
to shine.
This gives us
things like quasars,
supermassive black
holes in galaxy cores
that feed on a superheated
whirlpool of gas.
That accretion disk
shines so brightly
that we see them to the
ends of the universe.
Then there are X-ray binaries.
Sometimes the motion
of a visible star
reveals it to be in orbit
around a companion that
is dark invisible light but
bright in fluctuating X-ray
emission.
This happens when the
substance of a visible star
is accreting onto a companion
neutron star or black hole.
The most famous and the closest
is the Cygnus X-1 black hole,
6,000 light years away.
At around 15 times
the mass of the sun,
the dark object in
this system can't
be anything but a black hole.
The other famous black
hole in the Milky Way,
is of course, its own
supermassive black hole.
By the way, almost
all galaxies have
these lurking at their cores.
From our perspective,
that places it
in the constellation
of Sagittarius.
We call our supermassive
black hole Sagittarius A star.
Sag A star is visible
in X-rays, which
occasionally flash brighter as
it gobbles up a wisp of gas.
But more compellingly,
we've tracked
the motion of stars near the
galactic core for many years.
They show crazy slingshot orbits
around an empty patch of space.
These orbits tell us
that a dark something
of around four million solar
masses lurks in the center.
The recent observations
of gravitational waves
from a pair of merging
black holes by LIGO
could be considered our
first direct detection
of black holes.
However, some
upcoming studies are
expected to lead to even
better understanding.
The Event Horizon
Telescope is right now
in the process of mapping space
around the Milky Way's Sag
A star black hole.
The EHT isn't a
single telescope.
It's a collaboration
of currently nine
and eventually 12 or
more radio telescopes
distributed across the planets.
They use very long baseline
interferometry, VLBI,
to synthesize observations at
millimeter and submillimeter
wavelengths.
The effect is a
telescope thousands
of kilometers in
diameter, at least
in terms of its
spatial resolution.
EHT could currently
detect an orange
on the surface of
the moon, if oranges
were bright in microwaves.
This has enabled EHT to map
the strange magnetic field
structures around the
Sag A star black hole.
Now, the actual event
horizon is even smaller
than this insane resolution,
but EHT isn't finished yet.
It's expected that over
the next year or so,
as EHT brings more and
more telescopes online,
it will actually see the dark
circular shadow of the Sag A
star event horizon.
Interferometry is
going to be used
to study much smaller
black holes in our galaxy,
the remnants of dead stars.
These black holes
occasionally pass
in front of more distant
background stars,
gravitationally lensing
the star's light.
At visible wavelengths,
this should
look like a brightening
of the star,
an effect called microlensing.
But interferometry will enable
incredibly high-res mapping,
and the distant
star should appear
to split into two or four
images as its light passes
around the gravitational
field of the black hole.
Between the Event
Horizon Telescope
and microlensing studies,
and of course, more LIGO
gravitational
waves observations,
over the next few years,
we'll have mapped the space
around black holes in ways that
were once thought impossible.
Black holes definitely
exist, but these studies
will be powerful tests
of whether they behave
as predicted by Einstein's
general theory of relativity
or whether there are
tantalizing discrepancies.
OK, onto the challenge answer.
I proposed the following
unfortunate scenario.
An extremely advanced
alien race has
decided to destroy the
Earth by enveloping it
in a giant Kugelblitz, a black
hole made entirely of lights.
They direct an intense
shell of light inwards
towards the Earth.
It has enough energy
to produce a black hole
with a mass of 100,000 suns and
an event horizon that almost
reaches the moon's orbit.
We become aware of the
problem and develop
two possible solutions.
One-- Project Phoenix Egg is to
build a giant Dyson sphere just
outside the moon's orbit to
absorb the incoming radiation.
While two, Project Disco Ball,
proposes a satellite network
orbiting the Earth
at half the moon's
orbit radius, capable of
generating a reflective force
shield to bounce the pulse
back the way it came.
You've been called
in as a consultant
to help choose
between these options.
Which is the least
hopeless of these options?
I also asked you
to draw a Penrose
diagram to justify your choice.
And that's exactly
where we should start.
In the challenge
question, I showed you
the Penrose diagram for a star
collapsing into a black hole.
It looks like this.
I'm drawing only the right part
of the usual Penrose diagram
here.
You can think of the
verticalish lines
as representing
points in space that
are a constant distance
from our center point.
So one of those vertical
lines represents the surface
of a sphere of a given radius.
The surface of our
star is represented
by its starting radius
at t equals zero,
but as time moves
forward, the radius
shrinks as the star collapses.
Eventually, it gets small enough
for the event horizon to form.
On the Penrose
diagram, that horizon
extends both forwards
and backwards in time.
This is because there are
regions of the universe that
are doomed to end up
in the singularity
even before the true
event horizon forms.
They just can't travel
fast enough away
to get away before that happens.
However, only part of
this doomed triangle
above the collapsing
star's surface
actually has the crazy
spacetime behavior
of the interior of a black hole.
Now, OK, let's change this
to represent our death
by Kugelblitz situation.
Now, the collapsing star is
replaced with a collapsing
shell of light.
That shell takes
a 45-degree path,
as do all light speed things
on the Penrose diagram.
It looks like this.
When all of the
energy of that shell
is concentrated in
a volume smaller
than its own Swarzschild
radius, an event horizon
forms as spacetime flows
faster than the speed of light
towards that superdense
region of space.
The fun thing about
black holes made
this way is that the
interior region--
that sad, doomed little triangle
inside the collapsing shell--
doesn't even know
that anything is wrong
until the shell overtakes it.
Even after the true
event horizon forms,
there remains this shrinking
patch of normal flat spacetime.
In our Kugelblitz
scenario, Earth
won't even see the
incoming shell of light
until it reaches us.
Well, let's look
at the scenarios
for stopping the Kugelblitz
before it consumes the Earth.
First, the Penrose diagram
for Project Disco Ball.
We generate a perfectly
reflective sphere
at approximately half the radius
of the eventual event horizon.
Then we wait.
The light shell passes
the moon's orbit,
and a true event horizon forms.
Space below that shell
remains comfortably flat,
but above the
shell, spacetime is
cascading behind the shell
towards the soon to be formed
singularity.
When the light reaches
our reflective barrier,
it is indeed perfectly
reflected, straight back
into a region of
spacetime that will
carry even that light
inexorably downwards
to form the singularity.
See, once the event horizon
forms, all paths below it
lead to that singularity,
even outgoing light paths.
The only direction is down.
And on the Penrose
diagram, that's
seen as the future
light cone of everything
below the event horizon
leading to the singularity,
even of the reflected
light shell.
Our other plan was to
build a Dyson sphere just
outside the moon's orbit.
As you might be guessing,
this is the winner.
As long as the event
horizon has not yet formed,
the incoming light
can be stopped.
The Dyson sphere absorbs all
of the energy from the shell,
so it immediately gains the
entire mass equivalence,
100,000 suns worth.
Fortunately, I said that the
sphere was infinitely strong.
So somehow it
supports that weight.
Just above the sphere,
which is only a bit larger
than that event horizon
that was going to form,
the spacetime curvature
is pretty insane.
But it's not quite a black hole,
and so in principle, the sphere
doesn't have to collapse.
Note that the original
mass of the sphere
isn't going to add
enough to the 100,000
suns of the near Kugelblitz
to appreciably increase
the size of the event horizon.
If you see your name below,
we randomly selected you
from the correct submissions.
Email us at pbsspacetime at
gmail.com with your name,
mailing address,
US T-shirt size--
small, medium,
large, et cetera--
and let us know which
of these Ts you'd like.
We'll send you your just
reward for saving humanity.
Now, some of you may
still be wondering,
what about the
inside of the sphere?
Well, here, we're saved by
Newton's shell theorem, which
states that the gravitational
force inside a perfectly
symmetric shell is zero.
In Einsteinian terms, spacetime
is flat within the sphere.
Admittedly, there's
the slight problem
of having blocked out
the sun, but hey, we
just built an infinitely
strong Dyson sphere
and charged it with an
impossible amount of energy.
Maybe we can just
build a mini sun inside
after we blast the aliens
and save spacetime.
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