## The Maths of Time Travel [Physics/Maths]

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### The Maths of Time Travel [Physics/Maths]

I'm pretty sure that there are solutions to the general relativity equations that imply that time travel is possible. (wikipedia says so, and I've read about it a few times)

However, I cannot for the life of me remember what these conditions are, or where I might find them, or even better, explain them here.

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zealo
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theory is that objects with a velocity higher than c have a negative time component right?
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gmalivuk
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zealo wrote:theory is that objects with a velocity higher than c have a negative time component right?

Imaginary, actually, so perhaps not too helpful. (The time dilation factor is the square root of 1-(v/c)^2, so the square root of a negative number if v>c.)

Also, there aren't solutions to GR that allow anything to accelerate through c in its local frame, which means that even if ftl travel was also time travel, that way of doing it wouldn't be possible in a system consistent with GR.

I have heard of two specific solutions. One is if the entire universe were rotating. I believe this is the GÃ¶del metric. The other involves rotating cosmic strings (i.e. long, stringy black holes) around each other, creating closed timelike curves in the vicinity of where they pass.

These are obviously not really practical solutions, especially the one where the whole universe has to rotate. I think there are others that are more feasible (in that they only need a few galaxies' mass of negative energy to work, instead of the whole universe, for instance), but I don't know what they are.
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Herman
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I've read that you can time travel with a garden-variety rotating black hole, by using frame dragging to accelerate to a speed greater than c with respect to a faraway observer, while still traveling at less than c in the rotating frame. This allows you to travel back in time. Is that right?

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Yes, you can travel forward in time.

I mostly post over at LessWrong now.

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gmalivuk
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Herman wrote:I've read that you can time travel with a garden-variety rotating black hole, by using frame dragging to accelerate to a speed greater than c with respect to a faraway observer, while still traveling at less than c in the rotating frame. This allows you to travel back in time. Is that right?

I never was able to make much headway with the mathematics of the Kerr metric, but according to Wikipedia, you're right. The Kerr vacuum (which is what describes a rotating black hole) does indeed have some closed timelike curves associated with it. This means a massive particle can start at some point in space-time and return to that same point in its own future, which is basically a fancy way of saying it can travel back in time.
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NathanielK
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gmalivuk wrote:I have heard of two specific solutions. One is if the entire universe were rotating. I believe this is the GÃ¶del metric. The other involves rotating cosmic strings (i.e. long, stringy black holes) around each other, creating closed timelike curves in the vicinity of where they pass.
I've also heard of the Alcubierre metric, Krasnikov tubes, the Tipler cylinder, and, of course, wormholes.
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