Energy conditions on Standard Stationary Space-times

Abstract

Let $\operatorname{(M,g)}=(\mathbb{R}\times F,-\beta dt^{2}+dt\otimes g_{F}(\xi,.)+g_{F}(\xi,.)\otimes dt+g_{F})$ be a standard stationary space-time. We investigate conditions on some 2-tensors and a vector field on $F$ which guarantee that $\operatorname{(M,g)}$ satisfies certain energy conditions from general relativity.
Additionally, we address questions related to the presence of conjugate points in causal geodesics in $\operatorname{(M,g)}$.