The weak cosmic censorship conjecture and the Hoop conjecture in the case of the axially symmetric Einstein-Vlasov system

Håkan Andréasson (Chalmers U of Technology, Gothenburg)

Jun 12. 2023, 15:00 — 15:50

I will present results from two studies on the axisymmetric Einstein-Vlasov system where we investigate gravitational collapse. First, the role of the binding energy for determining the asymptotic faith of the solutions will be discussed and the weak cosmic censorship conjecture (WCCC) will be seriously tested in the case when the total angular momentum J satisfies |J|>M^2. I will then present results from a recent study on collapse of highly prolate initial data. Shapiro and Teukolsky initiated a similar study in 1991 where they found evidence that the WCCC was violated for sufficiently prolate initial data. More recently, independent studies of this problem have been carried out by Yoo, Harada and Okawa in 2017 and by East in 2019. A common feature in these works is that the initial data are dust-like. Dust can be considered as a singular case of Vlasov matter. I will discuss a crucial difference and the close similarity between these models. The original motivation by Shapiro and Teukolsky to study this problem is based on the Lin-Mestel-Shu instability for gravitational collapse of dust in Newtonian gravity. I will argue that the Lin-Mestel-Shu instability is not relevant for studying the weak cosmic censorship of the Einstein-Vlasov system. To investigate collapse of highly prolate configurations is nevertheless interesting in view of the Hoop conjecture. I will formulate the "only if" part of the Hoop conjecture in terms of the apparent horizon and I will present results that support the conjecture and the WCCC. Finally, the inverse Hoop conjecture suggested by Hod in 2020 will be discussed in the context of our results. This is a joint work with Ellery Ames and Oliver Rinne.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Spectral Theory and Mathematical Relativity (Thematic Programme)
Piotr T. Chruściel (U of Vienna)
Peter Hintz (ETH Zurich)
Alexander Strohmaier (U Leeds)
Steven Morris Zelditch † (Northwestern U Evanston)