Ori's conjecture on perturbations of two-ended Kerr data

Let $(\mathcal{M},g)$ be the maximal vacuum Cauchy development of sufficiently small perturbations of asymptotically flat two-ended Kerr data corresponding to parameters $0<|a|<M$. A future or past extension is an extension $(\widetilde{\mathcal{M}},\widetilde{g})$ of $\mathcal{M}$ with $C^0$ metric $\widetilde{g}$. Ori's conjecture. There exist both a future and past extension $(\widetilde{\mathcal{M}},\widetilde{g})$ such that $\partial\mathcal{M}$ is a bifurcate null cone in $\widetilde{\mathcal{M}}$ and all future, respectively past, incomplete geodesics in $\gamma$ pass into $\widetilde{\mathcal{M}}\setminus\mathcal{M}$. Moreover, for generic such perturbations, any $C^0$ extension has no $L^2$ Christoffel symbols in a neighbourhood of any point of $\partial\mathcal{M}$. This conjecture predicts a weakly singular Cauchy horizon for generic perturbations of subextremal Kerr, extending the corresponding symmetric-model picture; it remains open in the full vacuum, nonsymmetric setting.