Bilge, Ayse HumeyraDereli, TekinBaysazan, EmirBirkandan, Tolga2026-03-142026-03-1420261572-95750020-7748https://hdl.handle.net/20.500.12469/7778https://doi.org/10.1007/s10773-025-06228-7The 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.eninfo:eu-repo/semantics/openAccessIntegrabilityNewman-Penrose FormalismNUT SolutionArticle10.1007/s10773-025-06228-72-s2.0-105030445775