Hawking's singularity theorem for $C^{1,1}$-metrics
  We provide a detailed proof of Hawking's singularity theorem in the regularity class $C^{1,1}$, i.e., for spacetime metrics possessing locally Lipschitz continuous first derivatives. The proof uses recent results in $C^{1,1}$-causality theory and is based on regularisation techniques adapted to the causal structure. 
Michael Kunzinger, Roland Steinbauer, Milena Stojkovic, James A.   Vickers
gr-qc math-ph math.DG math.MP