We've observed that, from the point of view of your friend Penelope who remains safely outside of the black hole, it takes you an infinite amount of time to cross the horizon. We've also observed that black holes evaporate via Hawking radiation in a finite amount of time. So by the time you reach the horizon, the black hole will be gone, right?

Wrong. When we said that Penelope would see it take forever for you to cross the horizon, we were imagining a non-evaporating black hole. If the black hole is evaporating, that changes things. Your friend will see you cross the horizon at the exact same moment she sees the black hole evaporate. Let me try to describe why this is true.

Remember what we said before: Penelope is the victim of an optical illusion. The light that you emit when you're very near the horizon (but still on the outside) takes a very long time to climb out and reach her. If the black hole lasts forever, then the light may take arbitrarily long to get out, and that's why she doesn't see you cross the horizon for a very long (even an infinite) time. But once the black hole has evaporated, there's nothing to stop the light that carries the news that you're about to cross the horizon from reaching her. In fact, it reaches her at the same moment as that last burst of Hawking radiation. Of course, none of that will matter to you: you've long since crossed the horizon and been crushed at the singularity. Sorry about that, but you should have thought about it before you jumped in.

The equations of general relativity have an interesting mathematical property: they are symmetric in time. That means that you can take any solution to the equations and imagine that time flows backwards rather than forwards, and you'll get another valid solution to the equations. If you apply this rule to the solution that describes black holes, you get an object known as a white hole. Since a black hole is a region of space from which nothing can escape, the time-reversed version of a black hole is a region of space into which nothing can fall. In fact, just as a black hole can only suck things in, a white hole can only spit things out.

White holes are a perfectly valid mathematical solution to the equations of general relativity, but that doesn't mean that they actually exist in nature. In fact, they almost certainly do not exist, since there's no way to produce one. (Producing a white hole is just as impossible as destroying a black hole, since the two processes are time-reversals of each other.)

So far, we have only considered ordinary "vanilla" black holes. Specifically, we have been talking all along about black holes that are not rotating and have no electric charge. If we consider black holes that rotate and/or have charge, things get more complicated. In particular, it is possible to fall into such a black hole and not hit the singularity. In effect, the interior of a charged or rotating black hole can "join up" with a corresponding white hole in such a way that you can fall into the black hole and pop out of the white hole. This combination of black and white holes is called a wormhole.

The white hole may be somewhere very far away from the black hole; indeed, it may even be in a "different Universe" -- that is, a region of spacetime that, aside from the wormhole itself, is completely disconnected from our own region. A conveniently-located wormhole would therefore provide a convenient and rapid way to travel very large distances, or even to travel to another Universe. Maybe the exit to the wormhole would lie in the past, so that you could travel back in time by going through. All in all, they sound pretty cool.

But before you apply for that research grant to go search for them, there are a couple of things you should know. First of all, wormholes almost certainly do not exist. As we said above in the section on white holes, just because something is a valid mathematical solution to the equations doesn't mean that it actually exists in nature. In particular, black holes that form from the collapse of ordinary matter (which includes all of the black holes that we think exist) do not form wormholes. If you fall into one of those, you're not going to pop out anywhere. You're going to hit a singularity, and that's all there is to it.

Furthermore, even if a wormhole were formed, it is thought that it would not be stable. Even the slightest perturbation (including the perturbation caused by your attempt to travel through it) would cause it to collapse.

Finally, even if wormholes exist and are stable, they are quite unpleasant to travel through. Radiation that pours into the wormhole (from nearby stars, the cosmic microwave background, etc.) gets blueshifted to very high frequencies. As you try to pass through the wormhole, you will get fried by these X-rays and gamma rays