I just read in Landau-Lifshitz that the Kerr metric admits closed timelike curves in the region $r \in (0, r_{hor})$ where $r_{hor}$ is the event-horizon ( I am talking about the case $|M|>|a|$ (subextremal case) here ). Now, unfortunately they don't give an example of such a curve. Could anybody of you write down explicitly such a CTC so that I could go through the computation once by myself. I would really like to see this once.
If anything is unclear, please let me know.
Best Answer
See section 3.19 of Black Holes: An Introduction By Derek J. Raine, Edwin George Thomas
https://books.google.ca/books?id=O3puAMw5U3UC&pg=PA103&lpg=PA103&dq=kerr+schild+closed+timelike&source=bl&ots=elnzJu2ySm&sig=B4cWXIkib4fqbs0D7yA2YlZKE8A&hl=en&sa=X&redir_esc=y#v=onepage&q=kerr%20schild%20closed%20timelike&f=false
That book has an example: Boyer Lindquist coordinates: take an orbit where only phi is changing, then the proper time on that orbit is given by (a formula in the book) then we set r = just inside the ring singularity, and one gets a timelike dt > 0 path that is periodic.