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A basic extension of the exterior part of the extreme Reissner-Nordstroemsolution in terms of a continuous metric and gauge potential is constructed.This extension is not smooth at the null hypersurface given by theCauchy-Killing horizon which separates isometric copies of the exterior metric.The Maxwell-Einstein system of equations is satisfied only in a weak sense. Themanifold is topologically incomplete and the spherical symmetry is globallybroken down to an axial symmetry. This behaviour can be attributed to theeffect of a 'topological string', in the sense of a infinitesimally thin closedstringlike object 'sitting on the rim' of the black hole and holding it open bymeans of an accompanying impulsive gravitational wave. The resultingdifferentiable manifold and the corresponding horizons are not anymore simplyconnected, being 'pierced' by the strings.Comment: 28 pages, 4 figures, IOP macros (MYIOPART.CLS). Added appendix plus  two references. Accepted for publication by Class. Quant. Gravit

Nonanalytic extensions of the extreme Reissner–Nordström metric in terms of weak solutions