A coordinate-free approach to obtaining exact solutions in general relativity: The Newman-Unti-Tamburino solution revisited

TL;DR

This paper presents a coordinate-free method to characterize the NUT solution in general relativity, establishing its uniqueness by analyzing integrability conditions of Newman-Penrose equations without relying on specific coordinates.

Contribution

It introduces a novel coordinate-free approach to identify the NUT solution, providing a new perspective on its uniqueness in the context of Petrov Type D vacuum metrics.

Findings

The NUT solution is uniquely characterized by integrability conditions.

A coordinate-free characterization of the NUT solution is established.

The approach simplifies understanding of the solution's geometric properties.

Abstract

The Newman-Unti-Tamburino (NUT) solution is characterized as the unique Petrov Type $D$ vacuum metric such that the two double principal null directions form an integrable distribution. The uniqueness of the NUT is established by evaluating the integrability conditions of the Newman-Penrose equations up to $SL(2,\mathbb{C})$ transformations, resulting in a coordinate-free characterization of the solution.