Abstract: This thesis deals with questions of geometric rigidity and the existence of singularities in spacetimes. First, we extend the Hawking–Penrose singularity theorem to spacetime metrics of regularity C 1. In the cosmological case, Bartnik’s famous splitting conjecture asserts the rigidity of the Hawking–Penrose theorem, and has been shown to be equivalent to the existence of CMC Cauchy surfaces. We extend a construction of Bartnik to obtain a large class of cosmological spacetimes which, although timelike geodesically incomplete, contain no CMC Cauchy surfaces. Lastly, we present a generalization of the Lorentzian splitting theorem to the synthetic context of Lorentzian length spaces.
Singularities and rigidity in smooth and non-smooth spacetimes
29.10.2024 18:00 - 19:00
Organiser:
R. I. Boţ
Location:
Zoom