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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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