We construct a new class of plane-symmetric solutions possessing a curvature singularity which is null and weak, like the spacetime singularity at the Cauchy horizon of spinning (or charged) black holes. We then analyse the stability of this singularity using a rigorous non-perturbative method. We find that within the framework of (linearly-polarized) plane-symmetric spacetimes this type of null weak singularity is locally stable. Generically, the singularity is also scalar-curvature. These observations support the new picture of the null weak singularity inside spinning (or charged) black holes, which is so far established primarily on the perturbative approach.

17 pages, 2 PostScript figures, to appear in Phys. Rev. D