Penrose’s singularity theorem and the Kerr space-time

In this short paper, Penrose’s famous singularity theorem is applied to the Kerr space-time. In the case of the maximally extended space-time, the assumptions of Penrose’s singularity theorem are not satisfied as the space-time is not globally hyperbolic. In the case of the unextended space-time – defined up to some radius between the inner and outer event horizons – the assumptions of the theorem hold, but scalar curvature invariants remain finite everywhere. Calculations are done in detail showcasing the validity of the theorem, and we discuss how geodesic incompleteness does not necessarily imply a physical singularity. The simpler case of the Reissner-Nordström is used as an introductory example.