Extremal isolated horizons with $\Lambda$ and the related unique type D black holes

TL;DR

This paper generalizes the geometry of extremal isolated horizons to include a cosmological constant and relates these horizons to specific algebraic type D black holes, providing explicit geometric and physical parameter relations.

Contribution

It introduces a 6-parameter family of extremal isolated horizons in (anti-)de Sitter spacetimes and links them to extremal black holes within the type D class, including Kerr-Newman-NUT-(A)dS.

Findings

Derived a generalized induced metric for extremal isolated horizons with $ ext{(A)dS}$

Identified extremal horizons in Plebanski-Demianski spacetimes

Established relations between physical and geometric parameters of extremal horizons.

Abstract

We extend our previous work in which we derived the most general form of an induced metric describing the geometry of an axially symmetric extremal isolated horizon (EIH) in asymptotically flat spacetime. Here we generalize it to EIHs in asymptotically (anti-)de Sitter spacetime. The resulting metric conveniently forms a 6-parameter family which, in addition to a cosmological constant $\Lambda$, depends on the area of the horizon, total electric and magnetic charges, and two deficit angles representing conical singularities at poles. Such a metric is consistent with results obtained in the context of near-horizon geometries. Moreover, we study extremal horizons of all black holes within the class of Plebanski-Demianski exact (electro)vacuum spacetimes of the algebraic type D. In an important special case of non-accelerating black holes, that is the famous Kerr-Newman-NUT-(A)dS metric, we were able to identify the corresponding extremal horizons, including their position and geometry, and find explicit relations between the physical parameters of the metric and the geometrical parameters of the EIHs.