Spacetimes foliated by Killing horizons

TL;DR

This paper constructs exact solutions to Einstein and Einstein-Maxwell equations, showing spacetimes foliated by Killing horizons with special geometric properties, extending the understanding of horizon uniqueness and structure.

Contribution

It introduces a transformation that generates solutions with multiple Killing horizons, revealing new foliated spacetime structures with extremal horizon geometries.

Findings

Spacetimes are foliated by Killing horizons with a transversal horizon.

Constructed solutions have geometries matching extremal Kerr-Newman horizons.

Each solution admits multiple Killing vectors, indicating rich symmetry structures.

Abstract

It seems to be expected, that a horizon of a quasi-local type, like a Killing or an isolated horizon, by analogy with a globally defined event horizon, should be unique in some open neighborhood in the spacetime, provided the vacuum Einstein or the Einstein-Maxwell equations are satisfied. The aim of our paper is to verify whether that intuition is correct. If one can extend a so called Kundt metric, in such a way that its null, shear-free surfaces have spherical spacetime sections, the resulting spacetime is foliated by so called non-expanding horizons. The obstacle is Kundt's constraint induced at the surfaces by the Einstein or the Einstein-Maxwell equations, and the requirement that a solution be globally defined on the sphere. We derived a transformation (reflection) that creates a solution to Kundt's constraint out of data defining an extremal isolated horizon. Using that transformation, we derived a class of exact solutions to the Einstein or Einstein-Maxwell equations of very special properties. Each spacetime we construct is foliated by a family of the Killing horizons. Moreover, it admits another, transversal Killing horizon. The intrinsic and extrinsic geometry of the transversal Killing horizon coincides with the one defined on the event horizon of the extremal Kerr-Newman solution. However, the Killing horizon in our example admits yet another Killing vector tangent to and null at it. The geometries of the leaves are given by the reflection.