Strong cosmic censorship for surface-symmetric cosmological spacetimes with collisionless matter

TL;DR

This paper proves strong cosmic censorship for certain symmetric spacetimes with collisionless matter, showing it holds under various conditions on the cosmological constant and curvature, and characterizes black hole interior boundaries.

Contribution

It establishes strong cosmic censorship for surface-symmetric spacetimes with collisionless matter across different curvature and cosmological constant scenarios, including detailed boundary characterizations.

Findings

Strong cosmic censorship holds for $ ull\Lambda=0$ or $k extless0$, $ ull\Lambda extgreater0$ cases.

In expanding initial data, censorship is valid in the past for all parameters.

Small perturbations of Schwarzschild data do not produce Cauchy horizons from $i^+$.

Abstract

This paper addresses strong cosmic censorship for spacetimes with self-gravitating collisionless matter, evolving from surface-symmetric compact initial data. The global dynamics exhibit qualitatively different features according to the sign of the curvature $k$ of the symmetric surfaces and the cosmological constant $\Lambda$. With a suitable formulation, the question of strong cosmic censorship is settled in the affirmative if $\Lambda=0$ or $k\le0$, $\Lambda>0$. In the case $\Lambda>0$, $k=1$, we give a detailed geometric characterization of possible "boundary" components of spacetime; the remaining obstruction to showing strong cosmic censorship in this case has to do with the possible formation of extremal Schwarzschild-de Sitter-type black holes. In the special case that the initial symmetric surfaces are all expanding, strong cosmic censorship is shown in the past for all $k,\Lambda$. Finally, our results also lead to a geometric characterization of the future boundary of black hole interiors for the collapse of asymptotically flat data: in particular, in the case of small perturbations of Schwarzschild data, it is shown that these solutions do not exhibit Cauchy horizons emanating from $i^+$ with strictly positive limiting area radius.