  This paper concerns the hypersurface Bohm-Dirac model, i.e., the version of
Bohmian mechanics in a relativistic space-time proposed by D\"urr et al. [1],
which assumes a preferred foliation of space-time into spacelike hypersurfaces
(called the time foliation) as given. We show that the leaves of the time
foliation do not have to be smooth manifolds but can be allowed to have kinks.
More precisely, we show that, also for leaves with kinks, the trajectories are
still well defined and the appropriate $|\psi|^2$ distribution is still
equivariant, so that the theory is still empirically equivalent to standard
quantum mechanics. This result applies to the case where the time foliation is
determined by the previously proposed law $dn=0$, since such a foliation
generically has kinks.
