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Lurking in the depths of the mathematics of Einstein's general relativity
is an object even stranger than the mysterious black hole.
In fact, it's the black hole's mirror twin:
the white hole.
Some even think that these could be the origin of our universe.
The astrophysical phenomenon of the black hole has captured the imagination of scientist and science enthusiast alike
for many decades.
When the idea first emerged from Einstein's general theory of relativity,
physicists wondered how seriously to take this mathematical description of an inescapable region of spacetime.
Astronomers have since demonstrated that black holes are very real,
with convincing evidence that quasars, x-ray binaries, even the center of our own Milky Way galaxy
harbor these gravitational monstrosities.
But the mathematics that predicts the existence of the black hole also describes entities that are even stranger.
But whose relationship with reality is still unclear.
One such entity is the white hole.
A white hole is the "opposite" of a black hole, in a very literal, mathematical sense.
In fact, it's a time-reversed black hole.
A black hole is defined as a region of inward-flowing space-time with a one-way boundary called the event horizon,
from inside of which nothing can ever escape.
That makes a white hole a region of outward-flowing space-time.
It also has an event horizon, but that horizon prohibits entry, not exit.
Nothing outside a white hole can ever enter, and everything inside must be ejected.
Not even light can leave a black hole, hence the whole "black" thing.
But light can only leave a white hole.
So, these might be expected to radiate like crazy, and "white" would be an understatement.
Now, before everyone gets too excited,
white holes are probably a figment of mathematical imagination.
But they're a fascinating one.
And the idea may help us understand the origin of the universe.
White holes first emerged in the very earliest mathematical description of black holes.
Only a few months after Einstein published his general theory of relativity, Carl Schwarzhild solved its equations for a very particular case.
A single point of mass in an otherwise empty space-time.
The resulting Schwarzschild Metric
actually describes a black hole, the simplest black hole possible.
One without spin, without charge, or without change.
An eternal black hole, that doesn't grow or shrink,
and has always existed.
We've talked quite a bit about the bizarre behavior of space, and especially time, at and below the event horizon of a black hole.
Here's a little playlist if you want a refresher.
But here's the low-down.
The time that happens inside a black hole is not part of the past or future history of the outside universe.
From the perspective of an outside observer, any events occurring at the event horizon, including falling into it, happen infinitely far in the future.
Once you fall into the black hole, the Schwarzschild Metric tells us that space and time switch their roles.
The singularity no longer occupies a central location
it now occupies an inevitable future time.
Now, a real black hole form from the gravitational collapse of a massive star's core.
After the collapse, the "future singularity" comes into being.
And in the past, well, there's just a star.
But what does this idealized, eternal black hole look like in the past?
If we followed the Schwarzschild Metric back in time, we find something very strange.
We find the singularity again, lurking infinitely far in the past.
From the point of view of the outside universe, the eternal black hole's singularity exists in both the infinite future and infinite past.
That may sound strange, but it gets stranger.
To really understand what this eternal black hole looks like,
we're going to need to use a tool that we've already played with: the Penrose diagram.
To refresh your memory:
In a Penrose diagram, the x and y axes are redefined from space and time to merge space and time into new coordinates.
They compactify space-time so that time bunches up towards the edges and the borders correspond to infinite past and future.
Also, lines of constant distance and time curve, so that light paths always travel on 45 degree paths.
We are hanging out here and now, at the center of the diagram.
If we place an eternal black hole far to the left, then the future-left boundary represents the black hole's event horizon.
Any movement to the left brings you closer to that event horizon.
The event horizon itself is a 45 degree line.
In our weird Penrose coordinates, this represents a constant distance from the center of the black hole.
Light traveling at that 45 degree angle takes infinite time to escape the event horizon.
And the region beyond that line represents the interior of the black hole.
There, the dimensions of space and time switch roles.
The once-vertical contours of space are now time-like.
And flow inexorably towards the future singularity.
These two regions—our universe and the black hole interior—are just the Schwarzschild Metric mapped out using Penrose coordinates.
But our map isn't complete.
Remember, this is an eternal black hole, so it must exist in the past
Map into the past and we see a time-reflected version of our future black hole.
Everything about it is time-reversed.
The singularity is a past event.
Space within is time-like, but instead of flowing towards the singularity, it flows away.
And the event horizon is now a barrier to entry, not to exit.
We could make some sense of the behavior of this strange region by using the Penrose diagram.
Imagine: that something in our past was traveling at the speed of light and trying to reach the past event horizon.
There's no way it can get there, unless it goes faster than light.
Oh, it'll reach an event horizon, but only the event horizon of our future,
where it plunges into a regular black hole.
Remember, that all this is from our perspective, far from the event horizon.
We can never see anything cross the horizon;
the light rays from any crossing reach us infinitely far in the future.
Even if the black hole plunge began far in the past.
So, the past region of the eternal black hole has an event horizon that's a barrier to entry.
But also, light rays within that region must move up on the diagram.
That suggests they must exit into the outside universe.
Anything inside the past eternal black hole must be ejected.
So far, this region fits perfectly the description of a white hole.
The eternal black hole of the past technically is a white hole.
However, it's not one that we can ever observe.
For two reasons:
One: Light rays exiting that past white hole can never reach us.
The past singularity and past event horizon are infinitely far in the past from our point of view.
Light has to traverse infinite time to reach our location.
And two: there's no such thing as an eternal black hole.
The universe hasn't existed for eternity, and it didn't even begin with black holes in place.
Even though this type of white hole isn't observable, some physicists have taken the description very seriously.
The math describing the white hole is a perfectly good use of the Schwarzschild Metric.
It obeys general relativity.
It really is just a black hole, but if viewed backwards in time.
Yet general relativity is time-reversal symmetric.
Something that can happen forwards in time should also be able to happen in reverse.
So, can new white holes actually form?
Well, theoretically, yes, but to make one, you need to reverse entropy.
See, although it's possible to build a white hole in general relativity, there are other laws of physics the universe needs to obey,
For example, the 2nd law of thermodynamics.
It demands that entropy, a measure of disorder, always increase.
This law defines the direction of the flow of time.
To reverse time, you need to break the law.
You need to decrease entropy.
Now, this is technically possible because entropy is a statistical phenomenon.
Very rare reductions in entropy do happen, as long as globally, entropy increases on average.
It's conceivable that an incredibly rare entropy dip could lead to an effective reversal in time and a white hole could form.
However, it would immediately explode in a burst of energy as soon as entropy and time resumed their normal flow.
Upwards and forwards.
We actually did talk about a case where a random drop in entropy led to something very much like a white hole in this episode.
It's been speculated that the Big Bang itself came from such a profoundly improbable entropy dip.
And as it happens, the Big Bang looks, mathematically at least, much like a white hole.
It's an expanding outpouring of space-time, containing a vast amount of energy, and the Bang itself can never be entered.
After all, it's in the past.
The difference between the Big Bang and a white hole is that the former possesses no singularity.
It happened everywhere at the same time.
Still, that hasn't stopped physicists from having fun with the idea.
It's been proposed that when a black hole forms, a white hole forms on the opposite... "side".
Energy entering the black hole exits the white hole.
Physicist Lee Smolin takes it a step further to suggest that the resulting white hole is the Big Bang of a new, baby universe.
And that, in fact, our universe formed that way.
More on that another time.
But speaking of other universes...
It turns out that we haven't finished building our Penrose diagram yet.
The past white hole was revealed when we traced the eternal black hole backwards in time.
In fact, what we did was to "maximally extend" space-time.
We required that all paths be traceable through infinite past and future space, provided they don't hit the singularity.
But what about light rays entering or leaving our eternal black hole from the opposite side?
The mathematics of the Schwarzschild Metric describes an entirely independent region of space-time parallel to our own.
It looks like an identical alternate universe on the other side of the black hole.
Accessible through what we call an Einstein-Rosen bridge - better known as a wormhole.
In the not too distant future, we'll investigate the reality of this mysterious parallel patch of space-time.
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