The BKL Conjectures for Spatially Homogeneous Spacetimes

TL;DR

This paper rigorously constructs and analyzes a class of spatially homogeneous vacuum spacetimes, demonstrating their oscillatory behavior and causal structure, including the existence of a particle horizon.

Contribution

It provides a rigorous mathematical construction of Bianchi VIII and IX vacuum spacetimes exhibiting BKL oscillations and analyzes their causal properties.

Findings

Demonstrated oscillatory BKL behavior in constructed spacetimes

Established the existence of a particle horizon in these models

Analyzed the causal structure of the spacetimes

Abstract

We rigorously construct and control a generic class of spatially homogeneous (Bianchi VIII and Bianchi IX) vacuum spacetimes that exhibit the oscillatory BKL phenomenology. We investigate the causal structure of these spacetimes and show that there is a "particle horizon".