The paper “The Hawking-Penrose singularity theorem for C^{1,1} Lorentzian metrics” co-authored by Melanie Graf (Vienna), James Grant, Michael Kunzinger (Vienna), and Roland Steinbauer (Vienna), has just been published in the Communications in Mathematical Physics, link here.  The paper shows that the Hawking–Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continues to hold for Lorentzian metrics that are of $C^{1, 1}$-regularity.  The strategy of the proof requires a detailed analysis of the matrix Riccati equation for the approximating metrics, which may be of independent interest.