Strong cosmic censorship near Kerr in Christodoulou's square-integrable-connection formulation

For each fixed $M>0$, $0<|\mathfrak a|<M$ there is $\varepsilon>0$ such that, among smooth complete two-ended vacuum data $d$ with tenth weighted seminorm $p_{10}(d-d_*)<\varepsilon$ from the Kerr bridge data, those whose full maximal globally hyperbolic development has a future extension with continuous nondegenerate metric in $W^{1,2}_{\mathrm{loc}}$ form a meagre set in the weighted smooth topology. No symmetry is imposed and extensions need not be vacuum. Companions prove the weaker $C^2$ and $C^1$ versions. This is strong cosmic censorship in Christodoulou's formulation near Kerr only; it is not the global conjecture, and it does not treat one-ended or nonrotating data.

For each fixed $M>0$, $0<|\mathfrak a|<M$ there is $\varepsilon>0$ such that, among smooth complete two-ended vacuum data $d$ with tenth weighted seminorm $p_{10}(d-d_*)<\varepsilon$ from the Kerr bridge data, those whose full maximal globally hyperbolic development has a future extension with continuous nondegenerate metric in $W^{1,2}_{\mathrm{loc}}$ form a meagre set in the weighted smooth topology. No symmetry is imposed and extensions need not be vacuum. Companions prove the weaker $C^2$ and $C^1$ versions. This is strong cosmic censorship in Christodoulou's formulation near Kerr only; it is not the global conjecture, and it does not treat one-ended or nonrotating data.