Kerr–de Sitter Cauchy-horizon extendibility conjecture

Let $(\mathcal{M},g)$ be the maximal Cauchy development for the Einstein vacuum equations with positive cosmological constant of sufficiently small perturbations of subextremal Kerr–de Sitter data with $n$ black-hole regions and initial topology $\mathbb{S}^1\times\mathbb{S}^2$. Kerr–de Sitter extendibility conjecture. The spacetime is future, respectively past, extendible to $(\widetilde{\mathcal{M}},\widetilde{g})$ with $C^0$ metric $\widetilde{g}$, such that $\partial\mathcal{M}$ is the union of $n$ bifurcate null cones and all incomplete future, respectively past, inextendible geodesics of $\mathcal{M}$ pass into $\widetilde{\mathcal{M}}\setminus\mathcal{M}$. This is the vacuum analogue of the stated spherically symmetric Reissner–Nordström–de Sitter stability result and challenges strong cosmic censorship at low regularity for positive cosmological constant; the full assertion remains open.