  Antoci et al. have argued that the horizons of the boost-rotation, Kerr and
Schwarzschild solutions are singular, having shown that a certain
invariantly-defined acceleration scalar blows up at the horizons. Their
examples do not satisfy the usual definition of a singularity. It is argued
that using the same term is seriously misleading and it is shown that such
divergent functions are natural concomitants of regular horizons. In particular
it is noted that the divergence is given by the special relativistic
approximation to the overall metric. Earlier work on characterization of
horizons by invariants is revisited, a new invariant criterion for them is
proposed, and the relation of the acceleration invariant to the Cartan
invariants, which are finite at the horizons and completely determine the
spacetimes, is examined for the C-metric, Kerr and Schwarzschild cases. An
appendix considers coordinate identifications at axes and horizons.
