Marginally outer trapped tubes in de Sitter spacetime

TL;DR

This paper proves the instability of MOTSs in certain spacetimes and constructs complete MOTTs with constant mean curvature in de Sitter spacetime, showing their areas increase monotonically.

Contribution

It establishes the instability of MOTSs under specific conditions and demonstrates the existence of complete MOTTs with CMC sections in de Sitter spacetime.

Findings

All MOTSs in certain spacetimes are unstable.

Existence of complete MOTTs with CMC sections in de Sitter spacetime.

The area of these sections increases monotonically.

Abstract

We prove two results which are relevant for constructing marginally outer trapped tubes (MOTTs) in de Sitter spacetime. The first one holds more generally, namely for spacetimes satisfying the null convergence condition and containing a timelike conformal Killing vector with a "temporal function". We show that all marginally outer trapped surfaces (MOTSs) in such a spacetime are unstable. This prevents application of standard results on the propagation of stable MOTSs to MOTTs. On the other hand, it was shown recently that, for every sufficiently high genus, there exists a smooth, complete family of CMC surfaces embedded in the round 3-sphere S3. This family connects a Lawson minimal surface with a doubly covered geodesic 2-sphere. We show by a simple scaling argument that this result translates to an existence proof for complete MOTTs with CMC sections in de Sitter spacetime. Moreover, the area of these sections increases strictly monotonically. We compare this result with an area law obtained before for holographic screens.