  The general validity of the area law for black holes is still an open
problem. We first show in detail how to complete the usually incompletely
stated text-book proofs under the assumption of piecewise $C^2$-smoothness for
the surface of the black hole. Then we prove that a black hole surface
necessarily contains points where it is not $C^1$ (called ``cusps'') at any
time before caustics of the horizon generators show up, like e.g. in merging
processes. This implies that caustics never disappear in the past and that
black holes without initial cusps will never develop such. Hence black holes
which will undergo any non-trivial processes anywhere in the future will always
show cusps. Although this does not yet imply a strict incompatibility with
piecewise $C^2$ structures, it indicates that the latter are likely to be
physically unnatural. We conclude by calling for a purely measure-theoretic
proof of the area theorem.
