Marginal tubes and foliations by marginal surfaces

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.

18 pages. Accepted at Classical and Quantum Gravity

References in corpus (3)

• Isolated, slowly evolving, and dynamical trapping horizons: geometry and mechanics from surface deformations
• The intersection of a hyperplane with a lightcone in the Minkowski spacetime
• Emergence of Apparent Horizon in Gravitational Collapse

Cited by in corpus (1)

• Global regular null hypersurfaces in a perturbed Schwarzschild black hole exterior