Nonsingular extension of the Kerr-NUT–(anti–)de Sitter spacetimes

Due to the conical singularity along the symmetry axis Taub-NUT spacetimes suffer from a long and problematic history of physical interpretation. In 1969 Misner proposed a nonsingular interpretation taking advantage of the spacetime's topology and its underlying group-theoretic structure. We extend and refine his method to include a broader family of solutions and completely solve the outstanding issue of a nonsingular extension of the Kerr-NUT--(anti--)de Sitter solutions to Einstein's equations. Our approach relies on an observation that in 2 dimensional algebra of Killing vector fields there exist two distinguished vector fields that may be used to define $U(1)$-principal bundle structure over the nonsingular spaces of non-null orbits. For all admissible parameters we derive appropriate Killing vector fields and discuss limits to spacetimes with less parameters. The global structure of spacetime, together with nonsingular conformal geometry of the infinities is presented and (possibly also projectively nonsingular) Killing horizons is presented.