Seminarium Teorii Względności i Grawitacji

I will present a construction of extremal horizons with 3-sphere topology and a structure of U(1) principal bundle. A novel ingredient is that the fibres are transversal to the null geodesics of the horizon. Such horizons have local sections that are 2-spheres with conical singularities. Then the Einstein Equations constrain the intrinsic geometry of the horizon, consisting of the 2-metric and the rotation 1-form defined on the section. I will present the full family of horizon geometries admissible by this construction and compare the results with the Extremal Einstein Horizon equations present in the literature. Last but not least, the study of such horizons is motivated by the fact that they appear naturally in the Misner interpretation of the Plebański-Demiański spacetimes. As such, I will present the embedding of the abstract horizons into said spacetimes.