Seminarium Teorii Względności i Grawitacji

We investigate axisymmetric extremal isolated horizons (EIHs). They are described by an induced metric characterized by a single function. This function is subject to particular constraints following from Ricci identities in the Einstein-Maxwell theory. At first, we restrict our attention to asymptotically flat spacetimes. In the extremal case the solution is unique and depends on 5 independent parameters with direct geometrical or physical interpretation. The solution is possible to identify with extremal horizons in exact electrovacuum Plebański-Demiański spacetimes, that are all (double aligned) black holes of algebraic type D without a cosmological constant. Several interesting subclasses include accelerating extremely charged Reissner-Nordström black hole (C-metric) or extremal accelerating Kerr-Newman. As a natural extension, I will generalize the previous results to asymptotically (anti-) de Sitter spacetimes with non-zero cosmological constant and identify the EIHs geometry with the corresponding horizon geometry of a black hole in a special case of the famous Kerr-Newman-NUT-(A)dS metric.