On spacetime causality, globally hyperbolic spacetimes and Cauchy surfaces:
E. Minguzzi, Miguel Sánchez, The causal hierarchy of spacetimes, in: Recent Developments in Pseudo-Riemannian Geometry, EMS ESI Lectures in Mathematics and Physics 4 (2008) 299-358 [arXiv:gr-qc/0609119, ISBN:978-3-03719-051-7]
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, 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, 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, doi:10.1007/s11005-006-0091-5]
Review:
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