Non-singular Kerr-NUT-de Sitter spacetimes

We study Killing horizons and their neighbourhoods in the Kerr-NUT-(anti-)de Sitter and the accelerated Kerr-NUT-(anti-)de Sitter spacetimes. The geometries of the horizons have an irremovable singularity at one of the poles, unless the parameters characterising the spacetimes satisfy the constraint we derive and solve in the current paper. In the Kerr-NUT-de Sitter case, the constraint relates the cosmological constant of spacetime and the horizon area, leaving 3 parameters free. In the accelerated case the acceleration becomes a 4th parameter that allows the cosmological constant to take arbitrary value, independently of the area. We find that the neighbourhoods of the non-singular horizons are non-singular too, at least in the non-extremal case. Finally, we compare the embedded horizons with previously unembedded horizons provided by the local theory of type D Killing horizons to the second order.