The Schwarzschild Solution
The Schwarzschild Solution is used in General Relativity to describe the gravitational field around a static, non-rotating mass such as a black hole. It is named after Karl Schwarzschild, who found the exact solution to Einstein’s field equations in 1915. What the diagram above shows is what a visual representation of the Schwarzschild Solution looks like.
"Wow, look at that! Another universe right in our own back yard! I’ll pack my things and phone NASA!" was my immediate reaction to this concept.
Well, hold on - in order to understand how this stuff works, we need to first understand how to read the diagram. So let’s do some SCIENCE and figure it out.
First, what would you say if I asked you what this was?
Obviously you need to go back to first grade, you’d say, because clearly that’s the world. Well, I’d say, clearly it’s not. There’s no way Greenland is that big in comparison to Africa, and there’s no way that Australia is smaller than Alaska. In this picture, the north and south poles are lines instead of points like they are in real life. Plus, it’s flat. I think you’re the one who needs to go back to first grade.
The point I’m trying to make is that this is not an accurate representation of the world; in order to see it accurately, we’d need to cut it along the top and glue it to a sphere. It’s a little inconvenient to carry a globe around with us all the time, so we made this flat map to make our lives easier. We had to compensate reality in order to make the world easy to carry around, as we see with the size distortion.
Well, we have to compensate reality the same way in our “Travel Map” (or Kruskal diagram) if we wish to understand the Schwarzschild Diagram. Here it is, and sorry for the dinky little MS Paint drawings I had to make (I drew every picture except for the world, so bear with me).
Each colored line represents some form of travel.
»The orange line represents the kind of travel we encounter in our every day lives - driving to the store, say. You take a relatively long amount of time to travel a short distance.
»The blue line represents the Speed of Light - it’s also sitting at a 45 degree angle, which gives us a good reference point; anything less than 45 degrees relative to the vertical is physically possible (or at least we’ll say it is for the sake of argument, because traveling even close to the speed of light is a very tricky thing!).
»As the green line points out, very sophisticated, I know, it is impossible to travel faster than the speed of light, or rather to cover vast amounts of space in a short amount of time.
We can then apply this Travel Map to our Schwarzchild Diagram:
Yay! Look how pretty it is! Let’s analyze it!
» The orange line: You start out in our universe, Universe A. You make a stupid move and start traveling towards the black hole at regular human speeds. Stupid human! You cross the event horizon and immediately get crushed by the immense gravity at the singularity. Game over, buddy.
»The blue line: Somehow, you manage to reach the speed of light and head toward the black hole, but it only makes you meet your original fate even faster. Whoops.
»The green line: You head at the black hole with everything you’ve got, break the laws of physics, and safely pass through into Universe B. Congratulations! Oh, but I forgot. This is IMPOSSIBRU!!1!1
Okay, so traveling to another universe via black hole seems pretty futile. But, let’s remember, that this is a diagram of a static, non-rotating black hole. If we can remember back to middle school, lots of things are rotating - planets, stars, galaxies. The conservation of angular momentum shows us that as an ice skater twirls and brings her arms in, she begins to spin faster. As a star forms and collapses from interstellar gas, it also spins. If a massive star is spinning and then collapses, shouldn’t it be rotating hella fast? It better be! This means that, if we wish to realistically consider black holes for space travel, we must reconsider what our diagram should look like.
The Schwarzschild Solution for a rotating black hole has something called the Kerr solution attached to it (discovered by Roy Kerr in 1963). The Kerr Solution opens up an entirely different realm of possibilities concerning travel to more than one other universes - maybe even at measly human speeds! A multiverse of other universes finally seems physically possible, and easy to visualize, too.
But in the words of Richard Feynman: I gotta stop somewhere. I’ll leave you something to imagine!