Some Splitting Theorems for Stably Causal Spacetimes

We prove a splitting theorem for stably causal spacetimes and another splitting theorem for finitely compact spacetimes admitting a proper time synchronizable reference frame.     

Lorentzian Warped Products and Singularity

We show that to any convex function f: ⁿ there correspondinfinitely many geodesically complete metricsds² such that Ric() 0 for anynonspacelike vector . These metrics are constructedas the warped products of the natural metric in and the inner metric of a convexhyperface (the graph of f) in ^{n + 1}.