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In last week's episode, we looked at an extremely powerful
tool for understanding the strange space-time both
in and around black holes.
This is the Penrose diagram.
It compactifies our representation
of the dimensions of space and time,
allowing us to fit onto the one diagram
the infinitely stretched space-time
in the vicinity of a black hole's event horizon.
The Penrose diagram allows us to easily
understand the limits of our access to this universe.
That limit is defined by where something traveling
at the speed of light can get to, and the speed of light
is always at a 45-degree angle on this diagram.
Today, we are going to use the Penrose diagram to look
at the difference between the idealized, theoretical black
hole that we discussed in the previous episode
versus the real, astrophysical black holes that actually dwell
out there in the universe.
And then we'll use this knowledge
to address a very serious, although questionably
plausible, scenario involving an alien black hole attack.
The Penrose diagram we looked at represents a Schwarchild
black hole-- so no electric charge and no rotation,
but also an eternal black hole.
It always existed, never growing, never leaking.
Of course, there is no such thing.
At the very least, even a Schwarchild black hole
must have formed at some point.
A black hole forms when the core of a very massive star
collapses under its own gravity at the end of a star's life.
So what does this look like on a Penrose diagram?
Let's start with a nice, empty universe.
Empty, except for a single, giant star.
When the core of this star has fused all of its elements
into iron, it will start to collapse under its own weight.
There is a specific size that represents the point
of no return for this collapse.
This is the Schwarchild radius.
The larger the mass of the collapsing object,
the larger this radius.
If the star's core collapses to a size smaller
than its own Schwarchild radius, then the event horizon
forms, engulfing what's left of the star.
Below that horizon, but above the still-shrinking surface
of the star, space-time takes on the mad properties
of the black hole interior.
Space and time switch places, and the singularity soon forms,
with all space within the black hole flowing towards it faster
than the speed of light.
Outside the black hole, the event horizon
becomes the new edge of the universe on our Penrose
diagram.
The shape of space-time outside the horizon
warps to make this diagonal line,
a line of constant radius, the radius of the new black hole.
But here is something really weird.
There are regions in this otherwise normal space where
everything is doomed to fall into the singularity,
even though the black hole has not finished forming.
There's a region where all forward light cones only
include the singularity, even before the true event horizon
forms.
For anything in this region, there
isn't enough time to clear the impending event horizon,
even traveling at the speed of light.
On the Penrose diagram, we should
extend our effective event horizon backwards
to include that space.
This invisible horizon of doom grows
as the star shrinks and finally merges
with the true event horizon.
Any observers within this extended event horizon
are cut off from any future causal connection
with the rest of the universe.
Or are they?
OK, in the case of the collapsing start, that's still
a core, is going to be an insanely hot, dense place
and not great for observers.
But we can imagine a scenario in which the black hole is
about to fall around you, and yet you
are perfectly comfortable all the way up to, and even
briefly after, that happens.
Scenario-- a super-advanced alien civilization
decides to build a giant black hole that
will engulf the planet Earth.
It doesn't matter why.
I don't know.
They're light years away.
Maybe they just saw the first Star Wars prequel.
So these guys plan to destroy the Earth
with a kugelblitz, a black hole formed entirely from light.
Their spaceships form a sphere around the solar system
and blast a pulse of light inwards.
This gigantic shell of light descends around the earth
and will reach us in about a day.
Now, light has energy and so has a gravitational effect.
This blast has a mass-energy equivalence of 100,000 suns.
The Schwarchild radius of a black hole with this mass
is about one light second.
So the kugelblitz event horizon forms
just after the shell of light passes the moon.
At that point, it will look exactly
like a black hole from the outside.
From the inside, Earth has one second
in which it notices absolutely nothing wrong before it's
consumed in the singularity.
Why?
Because Newton's shell theorem tells us
that the entire inside of a spherically symmetric shell
of mass or energy feels no gravitational force
from that shell.
Space inside the collapsing kugelblitz
would remain comfortably flat until the collapsing
shell overtakes it, even after the event horizon forms.
So here is my challenge question.
Our own Homeworld Security agents discovered this plot,
so there's a chance we can do something.
Two competing plans are put forward.
Plan A is to build an infinitely-strong Dyson
sphere surrounding the earth just outside the moon's
orbital radius.
It would completely absorb the incoming pulse,
storing it as a ridiculous amount of electrical energy
and the accompanying increase in mass.
Maybe that energy can then power a super weapon
to fight the aliens.
Plan B is to launch a vast satellite network that
can produce a perfectly reflective, spherical force
shield about halfway between the Earth and the moon.
This shield will reflect all light outwards and uses
an impossible EM Drive technology that
allows it to ignore conservation of momentum,
so the satellites don't get ricocheted back to Earth.
Maybe the outgoing light wave will destroy the alien ships.
Let's assume that these plans can be executed,
but only exactly as described, and humanity has
to choose one, and only one.
You receive a conference call from various world leaders.
They've heard that you watched PBS Space Time,
and so they want your opinion on the plans.
Which do you recommend as slightly less hopeless?
Operation Phoenix Egg's Dyson Sphere or Operation Disco
Ball's Reflective Shield?
The president is especially upset,
so draw a nice Penrose diagram of the situation
to show why your preferred plan has the best shot.
Submit your carefully explained and diagrammed answer
to PBSSpaceTime@gmail.com within two weeks
of release of this episode for a chance
to win a Space Time t-shirt and, obviously, to save the world.
So assuming there's no kugelblitz apocalypse,
I'll see you next week for a new episode of Space Time.
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