### John Baez

Shared publicly -**An infinite corridor of universes**

Einstein's equations for gravity have some amazing solutions. Some describe things we see: the Big Bang and black holes. Others don't - like white holes, wormholes, and the infinite corridor of universes shown here.

As far as we know, all real-world black holes were formed at some moment in time by collapsing matter. But it's easier to find solutions of Einstein's equations that describe an eternal black hole whose shape doesn't change with time.

A rotating eternal black hole is called a

**Kerr black hole**, because this solution of Einstein's equation was first found by Roy Kerr in 1963. However, he just found part of the solution - not the whole picture here!

You see, when you solve Einstein's equations, you get a world obeying the rules of general relativity. But sometimes, if you're not careful, somebody else can find a bigger world that contains yours! It's like you drew a map of the world but you forgot there was anything south of the equator. A solution is called

**maximally extended**if you can't make it any bigger.

This picture shows the maximally extended Kerr solution. It's a

**Penrose diagram**, so moving up the page takes you forward in time, while moving to the right or left edge of the page takes you away from the black hole. Light moves along diagonal lines.

It's a single world, but it has portions called

**Universe**,

**Parallel Universe**,

**Antiverse**, and

**Parallel Antiverse**. Each of these is roughly like our universe, but with no Big Bang. Each lasts forever: time is not drawn to scale.

Each universe, and each parallel universe, has a black hole in it - and also a white hole! Each antiverse, and each parallel antiverse, has a black hole with

*negative mass*, and also a white hole with negative mass.

Only a few of these universes and antiverses are shown here. But there are infinitely many. The pattern repeats forever as you continue to go up or down the picture - that is, forwards or backwards in time.

There's also an infinite repeating sequence of black holes and white holes. And there's more - you can see singularities drawn as wiggly lines. But let's not worry about those yet. There's too much to take in at once.

Let's just follow the blue curve as it goes up the page. This describes a path you could take through space and time.

You could shoot out of a white hole at the very bottom of the picture and wind up in our universe.

Then you could jump into the black hole.

If you dodge the singularities, you could wind up in a new white hole!

And at this point, you have a choice. Swerve right and you go into a new universe. Swerve left and you go into a new parallel universe. They're different - but there's no big difference. In this picture, you choose to enter the new universe.

And so on!

It would be great fun if

*our*universe were part of a grand infinite corridor of universes like this. As far as we know, it's not. I suspect the real universe will be even more amazing. However, we will need much better science and technology to discover what's out there. Right now most of us are stuck here on Earth, and we need to learn to live here. That's a tough challenge too.

My picture is from Andrew Hamilton's wonderful website:

http://jilawww.colorado.edu/~ajsh/insidebh/penrose.html

I would like to tell you more about the Kerr black hole - but if I don't get around to it, also check out David Madore's page:

http://www.madore.org/~david/math/kerr.html

#physics

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29 comments

+Steve Wenner Electric charge creates electromagnetic fields, and electromagnetic fields carry energy, momentum and force, and these things are sources of gravity, just like matter is. And on the other side of the coin, the geometry of spacetime affects how electromagnetic fields propagate. So they very much interact in the dance.

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