``Nowhere'' differentiable horizons

Abstract

It is folklore knowledge amongst general relativists that horizons are well behaved, continuously differentiable hypersurfaces except perhaps on a negligible subset one needs not to bother with. We show that this is not the case, by constructing a Cauchy horizon, as well as a black hole event horizon, which contain no open subset on which they are differentiable.

28 pages, Latex with pstricks and graphicx, 4 ps figures

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