Closed trapped surfaces are important in general relativity in large part due to Penrose's incompleteness theorem.
The theorem states that: if a spacetime $(M, g)$ is globally hyperbolic, with a noncompact Cauchy hypersurface $H$ and a closed trapped surface $S$, and $\text{Ric}(N, N) \geq 0$ for all null vectors $N$, then $(M, g)$ is null geodesically incomplete.
This theorem is commonly (mis)quoted as a singularity theorem: it does not imply the existence of singularities, rather only that the spacetime is null geodesically incomplete. Many textbooks/notes are careful to note this fact. However, I can't think of any examples that back this caution up.
Are there explicit known examples of spacetimes which satisfy the hypotheses of this theorem, but which have no singularities?