Spacetimes foliated by non-expanding null surfaces in the presence of a cosmological constant

TL;DR

This paper classifies solutions to Einstein's equations with a cosmological constant that are foliated by non-expanding null surfaces, showing they belong to near horizon geometries, with results valid locally.

Contribution

It provides a local classification of Einstein solutions with null surface foliations, linking them to near horizon geometries in the presence of a cosmological constant.

Findings

Solutions are locally equivalent to near horizon geometries.

Foliations by non-expanding null surfaces imply near horizon structure.

Results hold in a neighborhood of a single null surface.

Abstract

We prove that every solution to Einstein's equations with possibly non-zero cosmological constant that is foliated by non-expanding null surfaces transversal to a single non-expanding null surface belongs to family of the near (extremal) horizon geometries. Our results are local, hold in a neighborhood of the single non-expanding null surface.