On spacetime causality, globally hyperbolic spacetimes and Cauchy surfaces:
Antonio N. Bernal, Miguel Sánchez, On smooth Cauchy hypersurfaces and Geroch’s splitting theorem, Commun. Math. Phys. 243 (2003) 461-470 [[arXiv:gr-qc/0306108v2](http://arxiv.org/abs/gr-qc/0306108), doi:10.1007/s00220-003-0982-6]
Antonio N. Bernal, Miguel Sánchez, Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes, Commun. Math. Phys. 257 (2005) 43-50 [[arXiv:gr-qc/0401112](https://arxiv.org/abs/gr-qc/0401112), doi:10.1007/s00220-005-1346-1]
Antonio N. Bernal, Miguel Sánchez, Further results on the smoothability of Cauchy hypersurfaces and Cauchy time functions, Lett. Math. Phys. 77 (2006) 183-197 [[arXiv:gr-qc/0512095](https://arxiv.org/abs/gr-qc/0512095), doi:10.1007/s11005-006-0091-5]