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

TL;DR

This paper investigates the formation of caustic singularities in Hořava-Lifshitz gravity, finding conditions under which such singularities are avoided or mitigated in different regimes and curvature scenarios.

Contribution

It provides a detailed analysis of caustic singularities in Hořava-Lifshitz gravity, highlighting the roles of IR and UV regimes, curvature, and the parameter λ in singularity formation.

Findings

No caustic singularities in IR limit with λ≠1.

Higher curvature terms can prevent caustics in UV regime with Ricci-flat spaces.

Curvature influences the effectiveness of higher curvature terms in avoiding caustics.

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.