Seminarium Teorii Względności i Grawitacji

In a spacetime containing an extremal horizon, the framework of isolated horizons or near-horizon geometries can be applied to study the intrinsic geometry of the horizon independently of the exterior spacetime. Building on work by Dunajski and Lucietti, we use this approach to prove that extremal horizons in a spacetime of arbitrary dimension and with general matter content are constrained by a rigidity theorem: any compact cross section of a rotating extremal horizon admits a Killing field. We discuss two applications of this result. Using the preferred Killing field, we construct new charged and rotating horizons in five dimensions carrying a Sasakian structure. We also propose a definition of higher multiplicity horizons and discuss the implications for the associated Aretakis instability.