Rigidity of time-flat surfaces in the Minkowski spacetime

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.

10 pages. To appear in Math. Res. Lett

References in corpus (3)

• Quasilocal mass in general relativity
• Isometric embeddings into the Minkowski space and new quasi-local mass
• Time flat surfaces and the monotonicity of the spacetime Hawking mass

Cited by in corpus (1)

• Time flat surfaces and the monotonicity of the spacetime Hawking mass