  We present investigations of a class of solutions of Einstein's field
equations close to the family of lambda-Taub-NUT spacetimes. The studies are
done using a numerical code introduced by the author elsewhere. One of the main
technical complication is due to the S3-topology of the Cauchy surfaces.
Complementing these numerical results with heuristic arguments, we are able to
yield some first insights into the strong cosmic censorship issue and the
conjectures by Belinskii, Khalatnikov, and Lifschitz in this class of
spacetimes. In particular, the current investigations suggest that strong
cosmic censorship holds in this class. We further identify open issues in our
current approach and point to future research projects.
