On the existence of marginally trapped tubes in spacetimes with local rotational symmetry

TL;DR

This paper proves that in certain symmetric spacetimes with non-zero rotation or twist, non-minimal marginally trapped tubes of a specific form cannot exist, contributing to the understanding of black hole horizons.

Contribution

It establishes a non-existence result for a class of marginally trapped tubes in locally rotationally symmetric spacetimes with non-zero rotation or twist.

Findings

Non-minimal marginally trapped tubes of the form $ ext{X}(t)$ cannot exist in these spacetimes.

The result applies to spacetimes with at least one non-zero rotation or spatial twist.

Provides insights into the structure of black hole horizons in symmetric spacetimes.

Abstract

Let $M$ be a locally rotationally symmetric spacetime with at least one of the rotation or spatial twist being non-zero. It is proved that $M$ cannot admit a non-minimal marginally trapped tube of the form $\chi=X(t)$.