English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider gravitational collapse for the axially symmetric Einstein-Vlasovsystem. We investigate the weak cosmic censorship conjecture in the case ofhighly prolate initial data and we investigate the ``only if" part of the Hoopconjecture. Shapiro and Teukolsky initiated a similar study in 1991\cite{Shapiro1991} where they found support that the weak cosmic censorshipconjecture was violated for sufficiently prolate spheroidal initial data. Morerecently, independent studies of this problem have been carried out by Yoo,Harada and Okawa \cite{Yoo2017} and by East \cite{East2019}. A common featurein these works is that the initial data are dust-like. Dust can be consideredas a \textit{singular} case of matter described by the Einstein-Vlasov system.The original motivation by Shapiro and Teukolsky to study this problem is basedon the Lin-Mestel-Shu instability for gravitational collapse of uniformspheroids in the case of dust in Newtonian gravity. We argue that theLin-Mestel-Shu solution is not relevant for studying the weak cosmic censorshipof the Einstein-Vlasov system and we argue that dust-like initial data is alsonot relevant. To investigate collapse of highly prolate spheroidalconfigurations for the Einstein-Vlasov system is nevertheless interesting inview of the Hoop conjecture. By choosing highly prolate initial data the weakcosmic censorship conjecture is seriously tested. We carry out such a study forinitial data which are not dust-like. We find formation of an apparent horizonin all cases we consider, which provides support for the weak cosmic censorshipconjecture. In our tests of the Hoop conjecture we compute the polarcircumference $\mathcal{C}_{H,p}$ at the time when the apparent horizon formsand find that it is less than 12% above $4\pi M$, where $M$ is the irreduciblemass of the apparent horizon, which agrees with the spirit of the Hoopconjecture.

On the Hoop conjecture and the weak cosmic censorship conjecture for the axisymmetric Einstein-Vlasov system