HORIZONS NON-DIFFERENTIABLE ON A DENSE SET

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