  There are at least four versions of Horava-Lishitz gravity in the literature.
We consider the version without the detailed balance condition with the
projectability condition and address one aspect of the theory: avoidance of
caustics for constant time hypersurfaces. We show that there is no caustic with
plane symmetry in the absence of matter source if \lambda\ne 1. If \lambda=1 is
a stable IR fixed point of the renormalization group flow then \lambda is
expected to deviate from 1 near would-be caustics, where the extrinsic
curvature increases and high-energy corrections become important. Therefore,
the absence of caustics with \lambda\ne 1 implies that caustics cannot form
with this symmetry in the absence of matter source. We argue that inclusion of
matter source will not change the conclusion. We also argue that caustics with
codimension higher than one will not form because of repulsive gravity
generated by nonlinear higher curvature terms. These arguments support our
conjecture that there is no caustic for constant time hypersurfaces. Finally,
we discuss implications to the recently proposed scenario of ``dark matter as
integration constant''.
