Non-singular extension of the Kerr-NUT-(anti) de Sitter spacetimes

Abstract

In 1963 Ezra Ted Newman and his two students Louis A. Tamburino, and Theodore W. J. Unti, proposed a deformation of the Shwarzschild spacetime that made it twisting. In the cosmological context, an equivalent solution had been found earlier, in 1951, by Abraham Haskel Taub. The problem that these solutions have is a conical singularity along the symmetry axis at all distances from the origin. In 1969 Misner proposed a non-singular interpretation of Taub-NUT spacetimes. We extend and refine his method to include a broader family of solutions and completely solve the outstanding issue of a non-singular 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 2 distinguished vector fields that may be used to define $U(1)$-principal bundle structure over the non-singular 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 non-singular conformal geometry of the infinities is presented and (possibly also projectively non-singular) Killing horizons is presented.

29 pages, 2 figures. CLarifications and figures were added

References in corpus (2)

• On the parameters of the Kerr-NUT-(anti-)de Sitter space-time
• Projectively non-singular horizons in Kerr-NUT-de Sitter spacetimes

Cited by in corpus (4)

• Symmetries of the asymptotically de Sitter spacetimes
• Conical singularity in spacetimes with NUT is observer-dependent
• Isolated horizons of the Hopf bundle structure transversal to the null direction, the horizon equations and embeddability in NUT-like spacetimes
• Vacuum Petrov type D horizons of non-trivial $U(1)$ bundle structure over Riemann surfaces with genus $>0$