The NOH conformal flatness conjecture

Let $(M,g)$ be a causal spacetime satisfying the No Observer Horizons condition (NOH). Its conformal group is denoted by $\mathrm{Conf}^\uparrow(M,g)$, and it is essential if there is no smooth positive function $\Omega$ such that $\mathrm{Conf}^\uparrow(M,g)\subseteq\mathrm{Isom}^\uparrow(M,\Omega g)$. NOH conformal flatness conjecture. If $\mathrm{Conf}^\uparrow(M,g)$ is essential, then $(M,g)$ is conformally flat. This is the proposed Lorentzian, non-compact analogue of the generalized Lichnerowicz conjecture under the stronger NOH assumption; the supplied text does not report a resolution.