Speaker: Walter Simon (Gravitational Physics, University of Vienna)
Title: Properties of marginally outer trapped surfaces in spacetime

Abstract:

A "marginally outer trapped surface" (MOTS) S in a spacetime is a compact
2-surface such that one of the two families of null geodesics emanating
orthogonally from S (called the outgoing one)  has vanishing expansion
everywhere on S. For an "outer trapped surface" (OTS) this expansion is
negative on S. OTS and MOTS play a role e.g. in the singularity theorems of
General Relativity by Hawking and Penrose.

I define and discuss "stability" for MOTS, in particular the property that an
interior neighbourhood of a stable MOTS can be foliated by OTS, whereas such
OTS are absent in an exterior neighbourhood. This result is based in essence
on properties of quasilinear and linear elliptic operators. Moreover, in a
spacetime foliated by hypersurfaces and with a MOTS on the initial leaf of the
foliation, I describe the propagation of this MOTS to adjacent leaves, which
depends crucially on its stability. Here the basic result is an application of
the implicit function theorem.