The time evolution of marginally trapped surfaces

TL;DR

This paper investigates the global behavior and evolution of marginally outer trapped surfaces (MOTS) in spacetime, demonstrating persistence, jump phenomena during coalescence, and regularity under certain conditions, with implications for understanding spacetime singularities.

Contribution

It provides new results on the persistence, coalescence, and regularity of MOTSs assuming the null energy condition, extending previous local existence results to a global context.

Findings

MOTS persist in future Cauchy surfaces containing them

Outermost MOTS can jump during coalescence events

Under generic conditions, the MOTS tube is smooth except at finitely many jumps

Abstract

In previous work we have shown the existence of a dynamical horizon or marginally trapped tube (MOTT) containing a given strictly stable marginally outer trapped surface (MOTS). In this paper we show some results on the global behavior of MOTTs assuming the null energy condition. In particular we show that MOTSs persist in the sense that every Cauchy surface in the future of a given Cauchy surface containing a MOTS also must contain a MOTS. We describe a situation where the evolving outermost MOTS must jump during the coalescence of two seperate MOTSs. We furthermore characterize the behavior of MOTSs in the case that the principal eigenvalue vanishes under a genericity assumption. This leads to a regularity result for the tube of outermost MOTSs under the genericity assumption. This tube is then smooth up to finitely many jump times. Finally we discuss the relation of MOTSs to singularities of a space-time.