Geometry Seminar: M. Graf (Hamburg)

Geometry Seminar (Geometric Analysis)

Speaker: Melanie Graf (Hamburg)

Title: Existence and uniqueness of ''nice'' maximal boundaries of spacetime

Abstract: Questions of (low-regularity) spacetime (in-)extendibility
have a long history within mathematical general relativity and are
closely related to several important physical problems such as strong
cosmic censorship and the nature of the incompleteness predicted from
the singularity theorems.
In case a spacetime is extendible at all it is therefore also essential
to gain an understanding of how much uniqueness may be expected from
purely geometric considerations (i.e., without assuming that the
extension continues to obey a specific physical model or similar).
Locally, this question was recently very comprehensively answered by
Sbierski. In my talk I will present a possible approach to the global
problem via considering certain extensions which are merely manifolds
with boundary. After introducing the problem we will discuss that, under
suitable assumptions on the regularity of the considered boundary
extensions and excluding the existence of ''intertwined geodesics'' in
the original spacetime, which is known to lead to rather pathological
situations, extendible spacetimes admit a unique maximal boundary
extension. This is based on joint work with Marco van den Beld Serrano.