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

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.