Strong cosmic censorship for T^2-symmetric cosmological spacetimes with collisionless matter

TL;DR

This paper proves strong cosmic censorship for T^2-symmetric cosmological spacetimes with collisionless matter, showing that such spacetimes are generically inextendible, thus supporting the conjecture in a specific symmetry class.

Contribution

It establishes the strong cosmic censorship conjecture for T^2-symmetric spacetimes with collisionless matter, extending previous results to a broader class.

Findings

Proves C^2-inextendibility of T^2-symmetric spacetimes with collisionless matter.

Demonstrates a rigidity property of Cauchy horizons inherited from Killing fields.

Supports the strong cosmic censorship conjecture in this symmetry setting.

Abstract

We prove strong cosmic censorship for T^2-symmetric cosmological spacetimes (with spatial topology T^3 and vanishing cosmological constant Lambda) with collisionless matter. Gowdy symmetric spacetimes constitute a special case. The formulation of the conjecture is in terms of generic C^2-inextendibility of the metric. Our argument exploits a rigidity property of Cauchy horizons, inherited from Killing fields.