Caustic singularity in Ho$\check {\textbf{r}}$ava-Lifshitz gravity

Abstract

In this note we searched for a family of solutions with Caustic singularity in non relativistic-renormalizable Ho$\check {\textbf{r}}$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 $\lambda\neq1$ 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 [JCAP 0909:005,2009] are satisfied correctly.