Strong Cosmic Censorship in orthogonal Bianchi class B perfect fluids and vacuum models

TL;DR

This paper proves the Strong Cosmic Censorship conjecture for orthogonal Bianchi class B perfect fluids and vacuum models, showing unbounded curvature invariants are generic and characterizing special symmetric solutions.

Contribution

It establishes the conjecture in this class by demonstrating generic unbounded curvature and analyzes solution behavior near the initial singularity using expansion-normalised variables.

Findings

Unbounded curvature invariants are generic in these models.

Bounded curvature occurs only in symmetric or plane wave solutions.

Most solutions converge to a specific Kasner parabola segment.

Abstract

The Strong Cosmic Censorship conjecture states that for generic initial data to Einstein's field equations, the maximal globally hyperbolic development is inextendible. We prove this conjecture in the class of orthogonal Bianchi class B perfect fluids and vacuum spacetimes, by showing that unboundedness of certain curvature invariants such as the Kretschmann scalar is a generic property. The only spacetimes where this scalar remains bounded exhibit local rotational symmetry or are of plane wave equilibrium type. We further investigate the qualitative behaviour of solutions towards the initial singularity. To this end, we work in the expansion-normalised variables introduced by Hewitt-Wainwright and show that a set of full measure, which is also a countable intersection of open and dense sets in the state space, yields convergence to a specific subarc of the Kasner parabola. We further give an explicit construction enabling the translation between these variables and geometric initial data to Einstein's equations.