# Symmetry axes of Kerr-NUT-(A)dS spacetimes

## TL;DR

This paper investigates the symmetry axes of higher-dimensional Kerr-NUT-(A)dS spacetimes, revealing singularities and closed timelike curves related to NUT charges, and introduces geometric tools to characterize these features.

## Contribution

It provides a detailed analysis of symmetry axes in Kerr-NUT-(A)dS spacetimes, identifying singularities and defining geometric quantities to characterize them, extending the understanding of spacetime structure.

## Key findings

- Some symmetry axes are necessarily singular with nonzero NUT charges.
- Regions with closed timelike curves surround the intersections of symmetry axes.
- New geometric quantities relate singularities to spacetime parameters.

## Abstract

We study fixed points of isometries of the higher-dimensional Kerr-NUT-(A)dS spacetimes that form generalizations of symmetry axes. It turns out that, in the presence of nonzero NUT charges, some parts of the symmetry axes are necessarily singular and their intersections are surrounded by regions with closed timelike curves. Motivated by similarities with the spacetime of a spinning cosmic string, we introduce geometric quantities that characterize various types of singularities on symmetry axes. Expanding the Kerr-NUT-(A)dS spacetimes around candidates for possible fixed points, we find the Killing vectors associated with generalized symmetry axes. By means of these Killing vectors we calculate the introduced geometric quantities describing axial singularities and show their relation to the parameters of the Kerr-NUT-(A)dS spacetimes. In addition, we identify the Killing coordinates that may be regarded as generalization of the Boyer-Lindquist coordinates.