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Minkowski space is the local model of 3 dimensionnal flat spacetimes. Recentprogress in the description of globally hyperbolic flat spacetimes showedstrong link between Lorentzian geometry and Teichm{\"u}ller space. We noticethat Lorentzian generalisations of conical singularities are useful for theendeavours of descripting flat spacetimes, creating stronger links withhyperbolic geometry and compactifying spacetimes. In particular massiveparticles and extreme BTZ singular lines arise naturally. This paper isthree-fold. First, prove background local properties which will be useful forfuture work. Second, generalise fundamental theorems of the theory of globallyhyperbolic flat spacetimes. Third, defining BTZ-extension and proving itpreserves Cauchy-maximality and Cauchy-completeness.

BTZ extensions of globally hyperbolic singular flat spacetimes