Rigidity of time-flat surfaces in the Minkowski spacetime

TL;DR

This paper investigates the rigidity properties of time-flat spacelike 2-surfaces in Minkowski spacetime, establishing local and global theorems that characterize their geometric behavior and uniqueness.

Contribution

It proves new local and global rigidity theorems for time-flat surfaces in Minkowski spacetime, extending the understanding of their geometric constraints.

Findings

Rigidity theorems for time-flat surfaces in Minkowski spacetime

Characterization of surfaces in static slices as time-flat

Extension of constant torsion analogy to spacetime surfaces

Abstract

A time-flat condition on spacelike 2-surfaces in spacetime is considered here. This condition is analogous to constant torsion condition for curves in three dimensional space and has been studied in [2, 4, 5, 12, 13]. In particular, any 2-surface in a static slice of a static spacetime is time-flat. In this article, we address the question in the title and prove several local and global rigidity theorems for such surfaces in the Minkowski spacetime.