# Constant scalar curvature hypersurfaces in $(3+1)$-dimensional GHMC Minkowski spacetimes

## TL;DR

This paper proves that most 3+1-dimensional GHMC Minkowski spacetimes admit a unique smooth foliation by spacelike hypersurfaces of constant scalar curvature, providing a canonical time function.

## Contribution

It establishes the existence and uniqueness of a constant scalar curvature foliation in non-trivial GHMC Minkowski spacetimes, extending previous results beyond special cases.

## Key findings

- Unique foliation by constant scalar curvature hypersurfaces
- Existence of a smooth time function with isochrones of constant scalar curvature
- Applicability to all GHMC Minkowski spacetimes except translation and Misner types

## Abstract

We prove that every $(3+1)$-dimensional flat GHMC Minkowski spacetime which is not a translation spacetime or a Misner spacetime carries a unique foliation by spacelike hypersurfaces of constant scalar curvature. In otherwords, we prove that every such spacetime carries a unique time function with isochrones of constant scalar curvature. Furthermore, this time function is a smooth submersion.