Trapped surfaces and symmetries

TL;DR

This paper proves that strictly stationary spacetimes in any dimension cannot contain closed trapped or marginally trapped surfaces, highlighting a fundamental geometric restriction related to symmetries.

Contribution

It establishes a general geometric theorem linking stationarity and the absence of trapped surfaces in arbitrary dimensions.

Findings

Strictly stationary spacetimes lack closed trapped surfaces.

The result applies in arbitrary dimensions.

Additional results on symmetries and trapped submanifolds are included.

Abstract

We prove that strictly stationary spacetimes cannot contain closed trapped nor marginally trapped surfaces. The result is purely geometric and holds in arbitrary dimension. Other results concerning the interplay between (generalized) symmetries and trapped submanifolds are also presented.