Projectively non-singular horizons in Kerr-NUT-de Sitter spacetimes

Abstract

It was recently discovered that Killing horizons in the generic Kerr-NUT-(anti) de Sitter spacetimes are projectively singular, i.e. their spaces of the null generators have singular geometry. Only if the cosmological constant takes the special value determined by the Kerr and NUT parameters, and the radius of the horizon, then the corresponding horizon does not suffer that problem. In the current paper, the projectively non-singular horizons are investigated. They are found to be cosmological and non-extremal. Every projectively non-singular horizon can be used to define a global completion of the Kerr-NUT-de Sitter spacetime it is contained in. The resulting spacetime extends from ${\mathcal{I}}^{-}$ to ${\mathcal{I}}^{+}$, has the topology of $\mathbb{R}\times S_3$ and is smooth except for a possible Kerr-like singularity.

arXiv comment11 pages

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Cited by in corpus (4)

• Non-singular extension of the Kerr-NUT-(anti) de Sitter spacetimes
• Uniqueness of extremal isolated horizons and their identification with horizons of all type D black holes
• 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 $>0$