Caustic Singularity in Horava-Lifshitz Gravity

In this note we search for a family of solutions with Caustic singularity in non relativistic-renormalizable HoA (TM) ava-Lifshitz (HL) theory without the general covariant. We show that in infrared (IR) limit and with a deviation from lambda=1 we have no caustic singularity. Also in ultraviolet (UV) regime and for Ricci flat 3-dimensional (3d) spaces and codimension 1 and for lambda not equal 1 the non linear terms should help bouncing this kind of most dangerous would be caustics. But if 3d curvature does not vanish, higher curvature terms do help caustics even in codimension one. Thus the arguments in (J. Cosmol. Astropart. Phys. 0909:005, 2009) are satisfied correctly.