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

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 $$\Phi _{01}=\Phi _{12}=0$$ Φ 01 = Φ 12 = 0 . We prove that these conditions determine the solutions up to a freedom in $$\Phi _{11}\pm 3\Lambda $$ Φ 11 ± 3 Λ .