2 00:00:03,070 --> 00:00:05,380 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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