Lightlike sets with applications to the rigidity of null geodesic incompleteness

Understand

An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses.

• Then, theorems with modified concusions may arise, showing that those conclusions will fail only in special cases, at least some of which may be described.
• These are the so-called rigidity theorems, and have many important examples in the especialized literature.
• In this paper, we prove rigidity results for generalized plane waves and certain globally hyperbolic spacetimes in the presence of maximal compact surfaces.