Generalized Lichnerowicz conjecture for compact Lorentzian manifolds

Let $M$ be a compact Lorentzian manifold, and let $\operatorname{Conf}(M,g)$ denote its conformal group. The group is essential if it does not act by isometries for any metric conformal to the Lorentzian metric $g$.

Generalized Lichnerowicz conjecture. If a compact Lorentzian manifold has an essential conformal group, then it is conformally flat.

This conjecture asks whether essential conformal dynamics force local conformal flatness in the compact Lorentzian setting. Known examples of compact Lorentzian manifolds with essential conformal groups are locally conformally equivalent, but the general local geometry remains open.