I have read that it's not possible.
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It is not possible, assuming that all tools we could use are "normal" in some particular sense (that is, they agree with some energy conditions). That means, they are made of particles and fields that cannot travel faster that light, for one example. Everything physicists discovered so far is "normal" in that sense, and it is highly unbelievable that we would come across something not "normal" in the future.
But if, theoretically, we are allowed to violate those conditions, then the answer is "we don't know". GR solutions are not explored enough in that area. I mention that to say that there is one possible loophole, though unlikely.
firtree
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