Totally umbilic null hypersurfaces in generalized Robertson-Walker spaces

TL;DR

This paper explores the geometric properties of null hypersurfaces in generalized Robertson-Walker spaces, establishing a correspondence with twisted decompositions and characterizing nullcones in specific cosmological models.

Contribution

It introduces a novel correspondence between totally umbilic null hypersurfaces and twisted decompositions, and characterizes nullcones in Friedmann and static spacetimes.

Findings

Nullcones are the only totally umbilic null hypersurfaces in the closed Friedmann model.

Established a correspondence between null hypersurfaces and fiber decompositions.

Applied geometric ideas to static spacetimes like Reissner-Nordström and Schwarzschild.

Abstract

We show that there is a correspondence between totally umbilic null hypersurfaces in generalized Robertson-Walker spaces and twisted decompositions of the fibre. This allows us to prove that nullcones are the unique totally umbilic null hypersurfaces in the closed Friedmann Cosmological model. We also apply this kind of ideas to static spaces, in particular to Reissner-Nordstr\"{o}m and Schwarzschild exterior spacetimes.