On the Counter-Rotation of Closed Timelike Curves

TL;DR

This paper examines the counter-rotation of closed timelike curves (CTCs) in rotating spacetimes, demonstrating that CTCs are counter-rotating relative to local angular velocity, challenging the notion that they are caused by source rotation.

Contribution

It provides a detailed analysis of CTCs in Kerr-Taub-NUT spacetime, showing their counter-rotation and questioning the causal interpretation related to source rotation.

Findings

CTCs are counter-rotating relative to local angular velocity.

This counter-rotation complicates the causal interpretation of CTCs.

The analysis uses Kerr-Taub-NUT spacetime as an example.

Abstract

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.