Extremal isolated horizons of the NUT type

TL;DR

This work introduces a new class of extremal isolated horizons with Hopf-bundle topology and null generators transversal to the bundle fibers, and solves the EEH equation on axisymmetric, conically singular horizons to classify intrinsic geometries (g, ω). It identifies three families of solutions (rotating with Λ≠0, rotating with Λ=0, and non-rotating) and derives admissible parameter ranges, then demonstrates embeddings into the Plebański-Demiański spacetimes and situates the results within the broader landscape by connecting to Petrov type D, Lucietti-Kunduri, and Podolský-Matejov solutions. The findings unify horizon topology and intrinsic geometry with known exact solutions, clarifying when and how these horizons can appear in physically relevant spacetimes. The results advance the understanding of extremal horizon geometry, their possible topologies, and their spacetime embeddings, with implications for exact solutions and black hole physics in generalized gravity settings.

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 Plebański-Demiański 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.

Figures (1)

• Figure 1: Admissible parameter values for the general rotating solution. For $\Lambda > 0$ all parameters outside of the outer circle are admissible. For $\Lambda < 0$ all values outside of the inner contour are admissible. We also exclude $\Omega\neq 0$.