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In this paper we argue that the well-known maximal extensions of the Kerr andKerr-Newman spacetimes characterized by a specific gluing (on disks) of twoasymptotically flat regions with ADM masses of opposite signs are physicallyinconsistent and actually non-analytic. We also discover a correct geometricalinterpretation of the surface $r=0$, $t={\rm const}$ - a dicone in the case ofthe Kerr solution and a more sophisticated surface of non-zero Gaussiancurvature in the case of the Kerr-Newman solution - which suggests that theproblem of constructing the maximal analytic extensions for these stationaryspacetimes is likely to be performed within the models with only oneasymptotically flat region, in which case a smooth crossing of the ringsingularity becomes possible, for instance, after carrying out an appropriatetransformation of the radial coordinate.

Are known maximal extensions of the Kerr and Kerr-Newman spacetimes physically meaningful and analytic?