Non-vacuum metrics for the Newman-Unti-Tamburino background: A coordinate-free approach to diverging and twisting solutions

TL;DR

This paper investigates non-vacuum metrics within the Newman-Unti-Tamburino (NUT) background, providing a coordinate-free characterization and classifying solutions under specific conditions related to divergence and twist.

Contribution

It introduces a coordinate-free approach to analyze diverging and twisting solutions in the NUT background, extending the understanding of Type D metrics beyond vacuum cases.

Findings

Characterizes NUT geometry as the unique Petrov Type D vacuum metric with integrable principal null directions.

Classifies expanding and twisting non-vacuum Type D metrics under specific null conditions.

Shows solutions are determined up to a certain freedom in the Ricci tensor component.

Abstract

The geometry of the Newman-Unti-Tamburino (NUT) vacuum solution is characterized as the unique Petrov Type D vacuum metric such that the two double principal null directions form an integrable distribution. We study expanding and twisting non-vacuum Type D metrics in this geometry, with the additional assumption $\Phi_{01}=\Phi_{12}=0$. We prove that these conditions determine the solutions up to a freedom in $\Phi_{11}\pm 3\Lambda$.