I understand that Kerr Black Holes are purely theoretical and have not been found anywhere in the Universe. However, they are theorized for possible means of time travel.
I am attempting to prove in a research paper that controlled time travel is statistically improbable for the human species. Therefore if scientists have evidence that there does not exist a black hole within a distance of X from Earth, and it is statistically improbable for the human species to ever be able to travel a distance of X, I can rule out time travel by means of kerr black holes with a significant degree of certainty.
However, I cannot find this "X" threshold, which is why I am asking this question. Have scientists verified that there are no kerr black holes within a distance of X from earth for some X?