On holonomy singularities in general relativity and the $C^{0,1}_{\mathrm{loc}}$-inextendibility of spacetimes

Understand

This paper investigates the structure of gravitational singularities at the level of the connection.

• We show in particular that for FLRW spacetimes with particle horizons a local holonomy, which is related to a gravitational energy, becomes unbounded near the big-bang singularity.
• This implies the $C^{0,1}_{\mathrm{loc}}$-inextendibility of such FLRW spacetimes.
• Again using an unbounded local holonomy we also give a general theorem establishing the $C^{0,1}_{\mathrm{loc}}$-inextendibility of spherically symmetric weak null singularities which arise at the Cauchy horizon in the interior of black holes.