# Algorithmic characterization results for the Kerr-NUT-(A)dS space-time. I. A space-time approach

## TL;DR

This paper introduces an algorithmic method to determine if a vacuum space-time admits a Killing vector field and is locally isometric to Kerr-NUT-(A)dS, with a focus on the Kerr-(A)dS case.

## Contribution

It provides a novel algorithmic approach to identify Kerr-NUT-(A)dS space-times based on the vanishing of the Mars-Simon tensor.

## Key findings

- Algorithm successfully detects Kerr-NUT-(A)dS space-times.
- Method applies to general vacuum space-times with a focus on Kerr-(A)dS.
- Provides a practical tool for classifying space-time geometries.

## Abstract

We provide an algorithm to check whether a given vacuum space-time $(\mathcal{M},g)$ admits a Killing vector field w.r.t. which the Mars-Simon tensor vanishes. In particular, we obtain an algorithmic procedure to check whether $(\mathcal{M},g)$ is locally isometric to a member of the Kerr-NUT-(A)dS family. A particular emphasis will be devoted to the Kerr-(A)dS case.