 Quote by byron178
do they exist in reality or in nature?
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Closed timelike curves are predicted to exist around the ring singularity in Kerr-Newman metric-
http://arxiv.org/PS_cache/arxiv/pdf/...708.2324v2.pdf
though this is technically a hypothesis (CTCs) within a hypothesis (Cauchy horizon) within a theory (black hole/event horizon).
The CTCs are also within a boundary called the turnaround radius which some predict is supposed to send an infalling object out through a (very hypothetical) white hole-
http://casa.colorado.edu/~ajsh/phys5770_08/bh.pdf (page 23)
so even at this level of prediction, there seems to be some level of protection from reaching the CTCs (though a white hole would be just as elusive as CTCs, it's normally best to say that the Cauchy horizon is the barrier of predictability).