Extremal isolated horizons of the NUT type

Abstract

We provide a construction of a new class of axisymmetric extremal isolated horizons admitting a structure of U(1)-principal fiber bundle over a two-sphere. In contrast to the previous examples, the null generators are assumed to be transversal to the bundle fibers. We impose the Einstein equations at the horizon and explicitly derive all intrinsic geometries of the extremal horizon, consisting of a two-sphere metric and a rotation 1-form, in the above class. The 2-geometries turn out to be equivalent to the classification of conically singular horizons with product topology. Both the rotating and non-rotating horizons are then embedded in the Pleba\'nski-Demia\'nski spacetimes, which naturally admit horizons of this type. Furthermore, we compare our results with previously obtained solutions to the Einstein vacuum extremal horizon equation with cosmological constant and the solution of Petrov type D equation with transversal bundle structure.