Splitting theorems for spatially closed space-times (Q1064556)

The author proves the following Lorentzian splitting theorem: Let V be a space-time which has the following properties. (A) V contains a compact Cauchy surface. (B) Ric(X,X)\(\geq 0\) for all timelike X. (C) V contains a complete timelike curve. (D) For each \(p\in V\), every future resp. past inextendible null geodesic issuing from p reaches a point in the timelike future resp. past of p. Then V splits into the pseudo-Riemannian product of \(({\mathbb{R}},-dt^ 2)\) and (M,h) where M is a smooth compact spacelike hypersurface with induced metric h. The proof employs methods developed by \textit{R. Bartnik} [Commun. Math. Phys. 94, 155-175 (1984; Zbl 0548.53054)] and \textit{C. Gerhardt} [ibid. 89, 523-553 (1983; Zbl 0519.53056)]. Several equivalent characterizations of condition (D) are given too.