Symmetric non-expanding horizons

TL;DR

This paper investigates symmetric non-expanding horizons in arbitrary dimensions, proving a rigidity theorem for helical symmetry and classifying 4D symmetric NEHs based on their symmetry groups.

Contribution

It formulates and proves a quasi-local Hawking rigidity theorem for NEHs with helical symmetry and classifies symmetric NEHs in 4D spacetimes based on their isometry groups.

Findings

Helical symmetry implies null and cyclic symmetries in NEHs.

Complete classification of symmetric NEHs in 4D based on symmetry groups.

Existence of a 2-sphere cross-section in classified NEHs.

Abstract

Symmetric non-expanding horizons are studied in arbitrary dimension. The global properties -as the zeros of infinitesimal symmetries- are analyzed particularly carefully. For the class of NEH geometries admitting helical symmetry a quasi-local analog of Hawking's rigidity theorem is formulated and proved: the presence of helical symmetry implies the presence of two symmetries: null, and cyclic. The results valid for arbitrary-dimensional horizons are next applied in a complete classification of symmetric NEHs in 4-dimensional space-times (the existence of a 2-sphere crossection is assumed). That classification divides possible NEH geometries into classes labeled by two numbers - the dimensions of, respectively, the group of isometries induced in the horizon base space and the group of null symmetries of the horizon.