I just saw this YouTube video (only 3 mins long) of Neil deGrasse Tyson explaining what happens when two black holes collide. He says that when the black holes are rotating around each other, there exists a path that you could follow that would cause you to travel back in time. Any chance that someone could explain this in an intuïtive way to me? I just finished my 1st bachelor physics, to give you an idea of my knowledge. I also understand the basics of special relativity.
I think he's being a bit loose with the truth.
There is a solution to Einstein's equations due to Kramer and Neugebauer$^1$ that describes two black holes rotating around each other. Well, sort of. I confess I don't really understand the details, but the two black holes have to be separated by a massless rod, so at best it would only be an approximation to a real binary black hole.
Anyhow, the setup can be described in a way analogous to a rotating cylinder, and consequently it warps spacetime in the same way that a Tipler cylinder does. Since the geometry near a Tipler cylinder has closed timelike curves that means the KN metric also has closed timelike curves.
However I was under the impression that Hawking had proved no finite system can have closed timelike curves unless exotic matter is involved (the Tipler cylinder is infinite) so I don't see how the KN metric can manage the trick. Maybe it's the artificial constraint of the massless bar connecting the two black holes. If so, this means that a real black hole binary will not have any closed timelike curves associated with it, and therefore no time travel. Sorry!
$^1$ Kramer D. and Neugebauer G., "The Superposition of Two Kerr Solutions," 1980, Phys. Lett. A, 75, 259 - I don't think this is available online.