On the Counter-Rotation of Closed Timelike Curves

While it is tempting to think of closed timelike curves (CTCs) around rotating bodies such as a black hole as being "caused" by the rotation of the source, Andr\'eka et al. pointed out that the underlying physics is not as straightforward since such CTCs are "counter-rotating", i.e., the time orientation (the opening of the local light cones) of the CTCs is opposite to the direction in which the singularity or the ergosphere rotates. It was also suggested that this is a generic phenomenon that calls for a deeper intuitive physical understanding. In this short note we point out -- with Kerr-Taub-NUT as an example -- that CTCs are counter-rotating with respect to the local angular velocity of the spacetime, which makes a physical interpretation of CTCs being "caused" by a rotating source even more problematic.