The scalar curvature flow in Lorentzian manifolds

TL;DR

This paper proves the existence of closed hypersurfaces with prescribed scalar curvature in globally hyperbolic Lorentzian manifolds, using barrier methods to establish the result.

Contribution

It introduces a new existence proof for prescribed scalar curvature hypersurfaces in Lorentzian geometry with barrier conditions.

Findings

Existence of hypersurfaces with prescribed scalar curvature

Application of barrier methods in Lorentzian manifolds

Extension of scalar curvature flow techniques

Abstract

We prove the existence of closed hypersurfaces of prescribed scalar curvature in globally hyperbolic Lorentzian manifolds provided there are barriers.