Marginal tubes and foliations by marginal surfaces

TL;DR

This paper introduces the concept of marginal tubes, generalizing black hole horizon notions, and proves that such tubes are null if all their spacelike sections are marginal surfaces, independent of topology or energy conditions.

Contribution

It defines marginal tubes as hypersurfaces foliated by marginal surfaces and establishes their nullity under broad conditions, extending the understanding of black hole horizons.

Findings

Marginal tubes are null if all spacelike sections are marginal surfaces.

The nullity result holds without topology or energy condition assumptions.

Uses double null coordinates to analyze spacelike surface geometry.

Abstract

In this paper, we introduce the notion of a marginal tube, which is a hypersurface foliated by marginal surfaces. It generalises the notion of a marginally trapped tube and several notions of black hole horizons, for example trapping horizons, isolated horizons, dynamical horizons, etc. We prove that if every spacelike section of a marginal tube is a marginal surface, then the marginal tube is null. There is no assumption on the topology of the marginal tube. To prove it, we study the geometry of spacelike surfaces in a 4-dimensional spacetime with the help of double null coordinate systems. The result is valid for arbitrary 4-dimensional spacetimes, regardless of any energy condition.