Abstract:
This thesis explores aspects of marginally outer trapped surfaces (MOTS) in cosmological
spacetimes, i.e. spacetimes with compact Cauchysurfaces. We first prove an instability
result for MOTS in a class of spacetimes containing a time like conformal Killing field with
a ’temporalfunction’. We then focus on de Sitter spacetime, where we establish an existence
result for a family of marginally outer trapped tubes (MOTTs) with constant mean
curvature sections of sufficiently high genus. In the second part, we extend a cosmological
singularity result by Galloway and Ling in several respects. First, we relax their assumption
on the Cauchy surface from being strictly 2-convex to 2-convex, now allowing for the
important case of time-symmetric Cauchy surfaces, leading to a characterization of
spacetimes whose Cauchy surfaces — or finite covers thereof —are surface bundles over
S 1 with totally geodesic fibers. Next, in the presence of a U (1) isometry , we further weaken
the 2-convexity requirement. Finally, these results are strengthened in special cases where
the Cauchy surface is Haken, non-prime, or nonorientable.

Zoom-Link
Meeting ID: 634 5076 0719
Passcode: 126380