A Coordinate-Free Approach to Obtaining Exact Solutions in General Relativity: The Newman-Unti-Tamburino Solution Revisited

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,C)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SL(2,\mathbb {C})$$\end{document} transformations, resulting in a coordinate-free characterization of the solution.