BTZ extensions of globally hyperbolic singular flat spacetimes

TL;DR

This paper explores BTZ extensions of flat spacetimes, establishing foundational properties, generalizing key theorems, and demonstrating that BTZ-extensions preserve important global properties like Cauchy-maximality and completeness.

Contribution

It introduces BTZ-extensions for flat spacetimes, proves their key properties, and extends the theory of globally hyperbolic flat spacetimes with new geometric insights.

Findings

BTZ-extensions preserve Cauchy-maximality

BTZ-extensions preserve Cauchy-completeness

Generalized fundamental theorems for flat spacetimes

Abstract

Minkowski space is the local model of 3 dimensionnal flat spacetimes. Recent progress in the description of globally hyperbolic flat spacetimes showed strong link between Lorentzian geometry and Teichm{\"u}ller space. We notice that Lorentzian generalisations of conical singularities are useful for the endeavours of descripting flat spacetimes, creating stronger links with hyperbolic geometry and compactifying spacetimes. In particular massive particles and extreme BTZ singular lines arise naturally. This paper is three-fold. First, prove background local properties which will be useful for future work. Second, generalise fundamental theorems of the theory of globally hyperbolic flat spacetimes. Third, defining BTZ-extension and proving it preserves Cauchy-maximality and Cauchy-completeness.