Revision 1

Accepted · first revision · record

Title: Is the generic Kerr Cauchy horizon a weak null singularity?
Plain: Inside a spinning black hole, disturbances pile up at an inner surface called the Cauchy horizon. The spacetime is known to stay continuous there, but it is not proved that it becomes too rough for Einstein's equations to continue beyond it.
Precise: For generic vacuum perturbations of subextremal Kerr ($0 < a < M$), Dafermos and Luk (2025) proved $C^0$ stability of the Cauchy horizon. Prove that for generic data the metric admits no continuous extension with Christoffel symbols in $L^2_{\mathrm{loc}}$ across the Cauchy horizon (the Christodoulou-Chrusciel formulation), i.e. that a weak null singularity forms. An answer is a proof of generic inextendibility or a counterexample.
Settled by: A proof that generic perturbations of Kerr produce blow-up of the $L^{2}$ norm of Christoffel symbols at the Cauchy horizon.
Kind: well-posed
Answer type: proof
References: (empty)
Literature status: partially-resolved
Status note: $C0$ stability proved (Dafermos and Luk, Annals 2025); generic $L^{2}$ Christoffel blow-up in vacuum without symmetry is open as of 2026.
Posed since: (empty)