Spacetimes foliated by Killing horizons
Tomasz Pawlowski, Jerzy Lewandowski, Jacek Jezierski

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…
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