In the Boyer-Lindquist-Block III (inside the inner event horizon) exists the so-called Carter time machine. There we can show that for every two points $p,q$ there exists a future-pointing timelike oder past-pointing timelike curves.

I'm not sure if I understood what "past-pointing" mean?

Why does this effect implies a "time machine"?


1 Answer 1


Suppose a spacetime has a global time function: a globally defined difference between past and future. Then we can divide timelike curves into two classes. When the proper time along a "future-pointing" curve advances, so does the global time. When the proper time along a "past-pointing" curve advances, the global time goes backwards.

In the Kerr-Carter time-machine there exist so-called "closed timelike lines" that reverse their temporal orientation. An observer along one of those lines starts off moving into the future, but ends up travelling into the past. Thus the term "time-machine": as my wristwatch time advances, the world around me seems to move backwards in time. I could in principle follow the curve for a while, and then change my acceleration to follow a different future-directed curve, effectively travelling back in time. Hence the term 'time machine'.

It's worth pointing out that Block 3 of the Kerr black hole has been shown to be generically unstable, so I wouldn't take this too seriously.

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    $\begingroup$ Can you explain or give me a reference to "generically unstable". I am studying the Kerr metric in an attempt to disprove the "time machine" and instability is last in my list of thoughts (it seems like a cheat). $\endgroup$
    – rrogers
    Jul 18, 2019 at 15:30

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