Spacelike hypersurfaces in twisted product spacetimes with complete fiber and Calabi–Bernstein-type problems

Abstract In this article spacelike hypersurfaces immersed in twisted product spacetimes $$I\times _f F$$ I × f F with complete fiber are studied. Several conditions ensuring global hyperbolicity presented, and a relation that needs to hold on each hypersurface be simple warped is also derived. When the assumed closed (compact without boundary) ambient spacetime has suitable expanding behaviour, non-existence results for constant mean curvature obtained. Under same hypothesis, characterization of compact maximal other totally umbilic ones restriction their full description one-dimensional Lorentzian included. Finally, equation graph computed as an application, some Calabi–Bernstein-type proven.